Classical Fourier Analysis

DOI10.1007/978-0-387-09432-8zbMath1220.42001OpenAlexW4293106097WikidataQ59411385 ScholiaQ59411385MaRDI QIDQ3508460

Loukas Grafakos

Publication date: 1 July 2008

Published in: Graduate Texts in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-09432-8

zbMATH Keywords

interpolationFourier transformdistributionmaximal functionsingular integraltorusLittlewood-Paley theorymultiplier\(L^p\) space

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces (42-01) Harmonic analysis in several variables (42Bxx)

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operators associated with Hankel and Hankel-Dunkl transforms ⋮ Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients ⋮ Low regularity well-posedness for the 3D generalized Hall-MHD system ⋮ A note on properties of the restriction operator on Sobolev spaces ⋮ Dorronsoro's theorem and a slight generalization ⋮ On the discrete spectrum of Schrödinger operators with Ahlfors regular potentials in a strip ⋮ Supersolutions for a class of nonlinear parabolic systems ⋮ Exponential decay of dispersion-managed solitons for general dispersion profiles ⋮ On some asymptotic formulas in the theory of concave compositions ⋮ A new characterization of Triebel-Lizorkin spaces on \(\mathbb{R}^n\) ⋮ A fractional Muckenhoupt-Wheeden theorem and its consequences ⋮ A sampling theory for non-decaying signals ⋮ Generalized Poisson summation formulas for continuous functions of polynomial growth ⋮ Sobolev-Jawerth embedding of Triebel-Lizorkin-Morrey-Lorentz spaces and fractional integral operator on Hardy type spaces ⋮ Neural network with unbounded activation functions is universal approximator ⋮ Martingale weak Orlicz-Karamata-Hardy spaces associated with concave functions ⋮ Vector valued maximal Carleson type operators on the weighted Lorentz spaces ⋮ Classification of solutions to a system of \(n^{\mathrm{th}}\) order equations on \(\mathbb{R}^n\) ⋮ Weighted Hankel transform and its applications to Fourier transform ⋮ Iterated weak and weak mixed-norm spaces with applications to geometric inequalities ⋮ Viscous flow around a rigid body performing a time-periodic motion ⋮ Martingale inequalities and fractional integral operator in variable Hardy-Lorentz spaces ⋮ Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates ⋮ On the compactness of oscillation and variation of commutators ⋮ Multilinear Fourier multipliers on variable Lebesgue spaces ⋮ A blow-up criterion for the strong solutions to the nonhomogeneous Navier-Stokes-Korteweg equations in dimension three. ⋮ Approximation properties of combination of multivariate averages on Hardy spaces ⋮ Extension of multilinear fractional integral operators to linear operators on mixed-norm Lebesgue spaces ⋮ The λ-cosine transforms with odd kernel and the hemispherical transform ⋮ Fourier multipliers for weighted \(L^2\) spaces with Lévy-Khinchin-Schoenberg weights ⋮ On the Witten index in terms of spectral shift functions ⋮ Sharp bounds for composition with quasiconformal mappings in Sobolev spaces ⋮ Hardy-Lorentz spaces for \(\mathbf{B}\)-valued martingales ⋮ A T(1) theorem for fractional Sobolev spaces on domains ⋮ Inhomogeneous oscillatory integrals and global smoothing effects for dispersive equations ⋮ Hitting probabilities for nonlinear systems of stochastic waves ⋮ A note on Hardy spaces and bounded linear operators ⋮ Decay estimate and well-posedness for the 3D Euler equations with Coriolis force ⋮ Fractional maximal operators with weighted Hausdorff content ⋮ A note on the embedding theorems for Sobolev-Lorentz spaces ⋮ \(L^p -L^q\) estimates for generalized spherical averages ⋮ On the Fourier dimension of \((d, k)\)-sets and Kakeya sets with restricted directions ⋮ \(L^p\)-\(L^q\) estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data ⋮ Algebraic structure of classical field theory: kinematics and linearized dynamics for real scalar fields ⋮ John-Nirenberg space on LCA groups ⋮ Stable blowup for the supercritical hyperbolic Yang-Mills equations ⋮ Elements of Postmodern Harmonic Analysis ⋮ Frame decomposition and radial maximal semigroup characterization of Hardy spaces associated to operators ⋮ Body-ordered approximations of atomic properties ⋮ On magnetic inhibition theory in non-resistive magnetohydrodynamic fluids ⋮ On compactness of commutator of multiplication and pseudodifferential operator ⋮ Mapping properties for operators on Herz-Morrey and Herz-Morrey-Hardy spaces ⋮ Approximation of non-decaying signals from shift-invariant subspaces ⋮ Convolution estimates for measures on some complex curves ⋮ Global well-posedness, BKM blow-up criteria and zero \(h\) limit for the 3D incompressible Hall-MHD equations ⋮ Edge states for generalized Iwatsuka models: magnetic fields having a fast transition across a curve ⋮ Eigenvalue bounds for non-self-adjoint Schrödinger operators with the inverse-square potential ⋮ Global stabilization of a 1D semilinear heat equation via modal decomposition and direct Lyapunov approach ⋮ Critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations ⋮ On (conditional) positive semidefiniteness in a matrix-valued context ⋮ Some estimates for \(p\)-adic rough multilinear Hausdorff operators and commutators on weighted Morrey-Herz type spaces ⋮ The IVP for a periodic generalized ZK equation ⋮ Beyond traditional Curvature-Dimension I: New model spaces for isoperimetric and concentration inequalities in negative dimension ⋮ The regularity problem for uniformly elliptic operators in weighted spaces ⋮ Marcinkiewicz interpolation theorem for spaces of Hardy type ⋮ On weak Mellin transforms, second degree characters and the Riemann hypothesis ⋮ Functional calculus for a bounded \(C_0\)-semigroup on Hilbert space ⋮ Maximal $L^p$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra ⋮ Wolff potential estimates for supersolutions of equations with generalized Orlicz growth ⋮ Strong solutions for the Cauchy problem to three-dimensional nonhomogeneous incompressible micropolar fluid equations with vacuum ⋮ Bias reduction in spot volatility estimation from options ⋮ Global solutions for a nonlinear integral equation with a generalized heat kernel ⋮ Cauchy problem for fractional advection-diffusion-asymmetry equations ⋮ Weighted inequalities for some integral operators with rough kernels ⋮ Atomic decomposition of vector Hardy spaces ⋮ Sharp inequalities for the Haar system and Fourier multipliers ⋮ An odd rearrangement of \(L^1(\mathbf{R}^n)\) ⋮ Inner functions in weak Besov spaces ⋮ Weighted \(L^p\) estimates for the area integral associated to self-adjoint operators ⋮ An application of weighted Hardy spaces to the Navier-Stokes equations ⋮ Factoring multi-sublinear maps ⋮ Analytic families of multilinear operators ⋮ $L^p$ mapping properties of the Bergman projection on the Hartogs triangle ⋮ Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth ⋮ A weak-Lp Prodi-Serrin type regularity criterion for the micropolar fluid equations ⋮ Riesz transform characterizations of Musielak-Orlicz-Hardy spaces ⋮ The Newtonian limit on cosmological scales ⋮ Homogeneous Campanato-Sobolev classes ⋮ Singular integrals with angular integrability ⋮ The predual and John-Nirenberg inequalities on generalized BMO martingale spaces ⋮ A uniqueness principle for up ≤ (−Δ)α 2u in the Euclidean space ⋮ On Fubini Type Property in Lorentz Spaces ⋮ Reconstruction and stability for piecewise smooth potentials in the plane ⋮ Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces ⋮ The Kato-Ponce Inequality ⋮ Banach algebra of the Fourier multipliers on weighted Banach function spaces ⋮ Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens ⋮ On the \(R\)-boundedness of stochastic convolution operators ⋮ New limiting absorption and limit amplitude principles for periodic operators ⋮ Sharp weighted bounds without testing or extrapolation ⋮ On the Hilbert transform of bounded bandlimited signals ⋮ Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces ⋮ Two-parameter version of Bourgain's inequality: rational frequencies ⋮ Elliptic equations with discontinuous coefficients in generalized Morrey spaces ⋮ Concentration and universal randomisation of proper subspaces ⋮ Sobolev multipliers, maximal functions and parabolic equations with a quadratic nonlinearity ⋮ Sharp estimates for the Szegő projection on the distinguished boundary of model worm domains ⋮ Local Hardy spaces of Musielak-Orlicz type and their applications ⋮ Explicit constants for hardy's inequality with power weight on \(n\)-dimensional product spaces ⋮ Hardy spaces \(H^p_L (\mathbb R^{n })\) associated with operators satisfying \(k\)-Davies-Gaffney estimates ⋮ Beltrami equations in the plane and Sobolev regularity ⋮ Weighted inequalities for fractional type operators with some homogeneous kernels ⋮ Bounded composition operator on Lorentz spaces ⋮ On Weyl's asymptotics and remainder term for the orthogonal and unitary groups ⋮ Applications of Littlewood-Paley theory for \(\dot{B}_\sigma\)-Morrey spaces to the boundedness of integral operators ⋮ On the boundedness of pseudo-differential operators on Triebel-Lizorkin and Besov spaces ⋮ Sobolev spaces and hyperbolic fillings ⋮ On fixed-domain asymptotics and covariance tapering in Gaussian random field models ⋮ Lipschitz linearization of the maximal hyperbolic cross multiplier ⋮ On Lebesgue integrability of Fourier transforms in amalgam spaces ⋮ Dichotomies for Lorentz spaces ⋮ Product BMO, little BMO, and Riesz commutators in the Bessel setting ⋮ Intrinsic structures of certain Musielak-Orlicz Hardy spaces ⋮ Extension and boundedness of operators on Morrey spaces from extrapolation techniques and embeddings ⋮ Nonuniqueness of weak solutions to the Navier-Stokes equation ⋮ Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound ⋮ Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability ⋮ Weak and strong type \(A_1\)-\(A_\infty \) estimates for sparsely dominated operators ⋮ Weighted Hardy spaces associated with elliptic operators. III: Characterisations of \(H_{L}^{p}({w})\) and the weighted Hardy space associated with the Riesz transform ⋮ Semi-linear fractional \(\sigma\)-evolution equations with mass or power non-linearity ⋮ Oracle inequalities and adaptive estimation in the convolution structure density model ⋮ Remarks on Liouville type theorems for the 3D steady axially symmetric Navier-Stokes equations ⋮ On correctors for linear elliptic homogenization in the presence of local defects: the case of advection-diffusion ⋮ Lower bound of Riesz transform kernels and commutator theorems on stratified nilpotent Lie groups ⋮ Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients ⋮ Dimension free bounds for the vector-valued Hardy-Littlewood maximal operator ⋮ On the global well-posedness of 3-D Boussinesq system with partial viscosity and axisymmetric data ⋮ The Lamm-Rivière system. I: \(L^p\) regularity theory ⋮ The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition ⋮ Sparse domination via the helicoidal method ⋮ Existence of weak solutions for a general porous medium equation with nonlocal pressure ⋮ Local well-posedness for the inhomogeneous nonlinear Schrödinger equation ⋮ A Hardy-Littlewood maximal operator for the generalized Fourier transform on \(\mathbb{R}\) ⋮ Norm inequalities for the Fourier coefficients of some almost periodic functions ⋮ Sharp gradient estimates for quasilinear elliptic equations with \(p(x)\) growth on nonsmooth domains ⋮ Fourier multiplier theorems involving type and cotype ⋮ Averaging operators along a certain type of surfaces with hypersingularity ⋮ On the constants for some fractional Gagliardo-Nirenberg and Sobolev inequalities ⋮ Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function ⋮ Averaged control for fractional ODEs and fractional diffusion equations ⋮ Quasi-monogenic functions ⋮ Weak type estimates for the noncommutative Vilenkin-Fourier series ⋮ Universal recovery maps and approximate sufficiency of quantum relative entropy ⋮ Generalized Gagliardo-Nirenberg inequalities using Lorentz spaces, BMO, Hölder spaces and fractional Sobolev spaces ⋮ Limited range multilinear extrapolation with applications to the bilinear Hilbert transform ⋮ Higher regularity of the ``tangential fields in the relativistic Vlasov-Maxwell system ⋮ On the effective properties of composite elastic plate ⋮ Energy identity and necklessness for a sequence of Sacks-Uhlenbeck maps to a sphere ⋮ A genuine analogue of the Wiener Tauberian theorem for some Lorentz spaces on \(\mathrm{SL}(2, \mathbb{R} )\) ⋮ Estimates for multilinear singular integral operators with nonsmooth kernels ⋮ Relating smoothness to expressions involving Fourier coefficients or to a Fourier transform ⋮ A Muckenhoupt's weight problem and vector valued maximal inequalities over local fields ⋮ Beyond Wiener's lemma: nuclear convolution algebras and the inversion of digital filters ⋮ Uncertainty principles for Fourier multipliers ⋮ Quantum differentiability on quantum tori ⋮ \(L^p-L^q\) multipliers on locally compact groups ⋮ Fourier spectrum of Clifford \(H^p\) spaces on \(\mathbb{R}_+^{n + 1}\) for \(1 \leq p \leq \infty \) ⋮ Orlicz-Lorentz Hardy martingale spaces ⋮ Poincaré inequalities for Littlewood-Paley operators ⋮ Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential ⋮ On the nonlinear Rayleigh-Taylor instability of nonhomogeneous incompressible viscoelastic fluids under \(L^{2}\)-norm ⋮ Hardy spaces \(H^p\) over non-homogeneous metric measure spaces and their applications ⋮ Long time dynamics of 2D quasi-geostrophic equations with damping in \(L^p\) ⋮ Hausdorff Besov-type and Triebel-Lizorkin-type spaces and their applications ⋮ Weights of exponential growth and decay for Schrödinger-type operators ⋮ An \(L_q (L_p)\)-theory for diffusion equations with space-time nonlocal operators ⋮ Equivalent norms of \(cmo^p(\mathbb{R}^n)\) and applications ⋮ Local well-posedness for the inhomogeneous nonlinear Schrödinger equation in \(H^s ( \mathbb{R}^n )\) ⋮ Weighted Fourier inequalities via rearrangements ⋮ On the second order derivative estimates for degenerate parabolic equations ⋮ Bilinear pseudo-differential operators with exotic symbols ⋮ Wolff potential estimates for Cheeger \(p\)-harmonic functions ⋮ Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system ⋮ Energy quantization of Willmore surfaces at the boundary of the moduli space ⋮ Topological properties of the set of functions generated by neural networks of fixed size ⋮ On compactness of commutators of multiplications and Fourier multipliers ⋮ Dual spaces for variable martingale Lorentz-Hardy spaces ⋮ A note on the behavior of the Dunkl maximal operator ⋮ Boundedness of sparse and rough operators on weighted Lorentz spaces ⋮ Hyperbolic wavelet analysis of classical isotropic and anisotropic Besov-Sobolev spaces ⋮ Conservation laws for even order elliptic systems in the critical dimension -- a new approach ⋮ On scale-invariant bounds for the Green's function for second-order elliptic equations with lower-order coefficients and applications ⋮ Almost everywhere convergence of multiple trigonometric Fourier series of functions from Sobolev classes ⋮ Optimal decay of \(p\)-Sobolev extremals on Carnot groups ⋮ Weighted norm inequalities in a bounded domain by the sparse domination method ⋮ Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE ⋮ The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions ⋮ Strichartz estimates in Wiener amalgam spaces and applications to nonlinear wave equations ⋮ Biparameter BMO under the action of a rotation ⋮ Boundedness and compactness of commutators associated with Lipschitz functions ⋮ On finite time blow-up for a 3D Davey-Stewartson system ⋮ Singular integrals in quantum Euclidean spaces ⋮ Optimal Fine-Scale Structures in Compliance Minimization for a Shear Load ⋮ On the real zeros of random trigonometric polynomials with dependent coefficients ⋮ Orlicz-Lorentz Spaces and their Composition Operators ⋮ Global Well-Posedness for Higher-Order Schrödinger Equations in WeightedL²Spaces ⋮ Maximal potentials, maximal singular integrals, and the spherical maximal function ⋮ Commutators, Little BMO and Weak Factorization ⋮ New variable martingale Hardy spaces ⋮ Unnamed Item ⋮ Generalized fractional maximal functions in Lorentz spaces Λ ⋮ 2-adic Valuations of Quadratic Sequences ⋮ Bochner–Riesz Means andK-Functional on Triebel–Lizorkin Spaces ⋮ Analysis of simultaneous inpainting and geometric separation based on sparse decomposition ⋮ Weighted inequalities for singular integral operators on the half-line ⋮ Optimal critical exponent L^p inequalities of Hardy type on the sphere via Xiao's method ⋮ Dimension free bounds for the Hardy–Littlewood maximal operator associated to convex sets ⋮ A new approach to bounds on mixing ⋮ Scaled oscillation and level sets ⋮ Maximum-norm stability of the finite element method for the Neumann problem in nonconvex polygons with locally refined mesh ⋮ An Analytical Study of Flatness and Intermittency through Riemann's Nondifferentiable Functions ⋮ A weak type $(1,1)$ estimate for the Hilbert operator in higher-dimensional setting ⋮ Lower semi-continuity for 𝒜-quasiconvex functionals under convex restrictions ⋮ Some variants of the Hardy inequality ⋮ Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities ⋮ Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence* ⋮ Global-in-time smoothing effects for Schrödinger equations with inverse-square potentials ⋮ Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation ⋮ Upscaling and spatial localization of non-local energies with applications to crystal plasticity ⋮ On the Oseen-Type Resolvent Problem Associated with Time-Periodic Flow past a Rotating Body ⋮ Norms supporting the Lebesgue differentiation theorem ⋮ Scattering properties of two singularly interacting particles on the half-line ⋮ Integral Menger curvature and rectifiability of $n$-dimensional Borel sets in Euclidean $N$-space ⋮ Stochastic Navier-Stokes-Fourier equations ⋮ Weighted estimates for the Calderón commutator ⋮ On Stokes--Ritz Projection and Multistep Backward Differentiation Schemes in Decoupling the Stokes--Darcy Model ⋮ The linear canonical wavelet transform on some function spaces ⋮ Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces ⋮ HARDY SPACES ON METRIC MEASURE SPACES WITH GENERALIZED SUB-GAUSSIAN HEAT KERNEL ESTIMATES ⋮ Simplices and sets of positive upper density in $\mathbb {R}^d$ ⋮ Unnamed Item ⋮ Global Well-Posedness and Scattering for Mass-Critical, Defocusing, Infinite Dimensional Vector-Valued Resonant Nonlinear Schrödinger System ⋮ Time-Periodic Linearized Navier–Stokes Equations: An Approach Based on Fourier Multipliers ⋮ Weak type operator Lipschitz and commutator estimates for commuting tuples ⋮ On stability of weak Navier–Stokes solutions with largeL^3,∞initial data ⋮ Estimates for parametric Marcinkiewicz integrals on Musielak-Orlicz Hardy spaces ⋮ Bilinear decompositions for products of Hardy and Lipschitz spaces on spaces of homogeneous type ⋮ Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces ⋮ Commutator criteria for strong mixing ⋮ Sharp Quantitative Weighted $$\mathop {\mathrm {BMO}}$$ Estimates and a New Proof of the Harboure–Macías–Segovia’s Extrapolation Theorem ⋮ Analysis of Viscous Fluid Flows: An Approach by Evolution Equations ⋮ Weighted complete continuity for the commutator of Marcinkiewicz integral ⋮ Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case ⋮ Conditional expectation type operators and modular inequalities ⋮ Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed ⋮ Gadjieva's conjecture, K -functionals, and some applications in weighted Lebesgue spaces ⋮ Weighted anisotropic product Hardy spaces and boundedness of sublinear operators ⋮ Inclusion between generalized Stummel classes and other function spaces ⋮ On a dual property of the maximal operator on weighted variable 𝐿^{𝑝} spaces ⋮ Exponential instability in the fractional Calderón problem ⋮ Spatially independent martingales, intersections, and applications ⋮ Radiating and non-radiating sources in elasticity ⋮ Complex interpolation with Dirichlet boundary conditions on the half line ⋮ Norm estimates for Bessel-Riesz operators on generalized Morrey spaces ⋮ The Maximal Singular Integral: Estimates in Terms of the Singular Integral ⋮ Unnamed Item ⋮ Another approach to the thin-film Γ-limit of the micromagnetic free energy in the regime of small samples ⋮ Unnamed Item ⋮ Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra ⋮ Time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space with a non-zero drift term: Asymptotic profile at spatial infinity ⋮ Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces ⋮ Global Well-Posedness for a Nonlocal Gross–Pitaevskii Equation with Non-Zero Condition at Infinity ⋮ On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations ⋮ Boundedness of fractional integral operator with rough kernel on generalized Morrey space ⋮ A COMPACTNESS PRINCIPLE FOR MAXIMISING SMOOTH FUNCTIONS OVER TOROIDAL GEODESICS ⋮ Long-Term Regularity of Two-Dimensional Navier--Stokes--Poisson Equations ⋮ Real Variable Methods in Harmonic Analysis and Navier–Stokes Equations ⋮ A Nonlocal Image Inpainting Problem Using the Linear Allen–Cahn Equation ⋮ Instability of the abstract Rayleigh–Taylor problem and applications ⋮ Logarithmic uncertainty principle for the Hankel transform ⋮ Phase-resolved ocean wave forecast with ensemble-based data assimilation ⋮ A note on weighted estimates for bilinear fractional integral operators ⋮ Approximation properties of combination of multivariate averages on Triebel-Lizorkin spaces ⋮ On the spatially asymptotic structure of time-periodic solutions to the Navier–Stokes equations ⋮ On a Fractional Version of a Murat Compactness Result and Applications ⋮ Best constants in some estimates for the harmonic maximal operator on the real line ⋮ Smoothness of functions versus smoothness of approximation processes ⋮ Solvability in weighted Lebesgue spaces of the divergence equation with measure data ⋮ Asymptotic expansion of the L 2 -norm of a solution of the strongly damped wave equation in space dimension 1 and 2 ⋮ Edge States for the Magnetic Laplacian in Domains with Smooth Boundary ⋮ Scattering by Curvatures, Radiationless Sources, Transmission Eigenfunctions, and Inverse Scattering Problems ⋮ Unnamed Item ⋮ A Multiplicity Result for a Non-Homogeneous Subelliptic Problem with Sobolev Exponent ⋮ Weighted 𝐿² inequalities for square functions ⋮ Joint estimation of Robin coefficient and domain boundary for the Poisson problem ⋮ On solvability in the small of higher order elliptic equations in grand-Sobolev spaces ⋮ A revisit on the compactness of commutators ⋮ Square roots of the Bessel operators and the related Littlewood–Paley estimates ⋮ Remark on the Chain rule of fractional derivative in the Sobolev framework ⋮ Nonparametric needlet estimation for partial derivatives of a probability density function on the d -torus ⋮ Lp$L^p$ bound for the Hilbert transform along variable non‐flat curves ⋮ Traces of some weighted function spaces and related non‐standard real interpolation of Besov spaces ⋮ Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average ⋮ Boundedness of the Calderón commutator with a rough kernel on Triebel-Lizorkin spaces ⋮ Bessel-Riesz operators on Lebesgue spaces and Morrey spaces defined in measure metric spaces ⋮ Falling drop in an unbounded liquid reservoir: steady-state solutions ⋮ Weak limits of fractional Sobolev homeomorphisms are almost injective ⋮ Dispersive estimates for the Schrödinger equation with finite rank perturbations ⋮ Real interpolation of variable martingale Hardy spaces and BMO spaces ⋮ The Cauchy problem for the critical inhomogeneous nonlinear Schrödinger equation in \(H^s(\mathbb{R}^n)\) ⋮ Final state observability in Banach spaces with applications to subordination and semigroups induced by Lévy processes ⋮ Detectability and global observer design for 2D Navier-Stokes equations with uncertain inputs ⋮ Global existence of weak solutions for 3D incompressible inhomogeneous asymmetric fluids ⋮ Uniform estimates for systems of elasticity in homogenization ⋮ Connection between weighted tail, Orlicz, Grand Lorentz and Grand Lebesgue norms ⋮ On Kakeya's maximal function. II: High dimensional cases ⋮ Transference and restriction of bilinear Fourier multipliers on Orlicz spaces ⋮ Periodic and almost periodic motions of Navier-Stokes flows and their stability in a perturbed half-space ⋮ Local and multilinear noncommutative de Leeuw theorems ⋮ Homogenization of high-contrast composites under differential constraints ⋮ Nonparametric identification and estimation of heterogeneous causal effects under conditional independence ⋮ Global existence and scattering for nonlinear Schrödinger equations with time-dependent damping ⋮ Velocity averaging for diffusive transport equations with discontinuous flux ⋮ Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications ⋮ Multi-component separation, inpainting and denoising with recovery guarantees ⋮ Weak solutions for the Stokes system for compressible non‐Newtonian fluids with unbounded divergence ⋮ Local and global existence in L^p for the inhomogeneous nonlinear Schrödinger equation ⋮ On the Democracy inequality for Haar systems and some geometric and analytical properties in Herz spaces on dyadic settings ⋮ Moment propagation of the plasma-charge model with a time-varying magnetic field ⋮ WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS ⋮ Asymptotic regularity for the generalized MHD‐Boussinesq equations ⋮ Variable Hardy–Lorentz martingale spaces Hp(·),q(·)$\mathcal {H}_{p(\cdot ),q(\cdot )}$ ⋮ The boundedness of operators on weighted multi-parameter local Hardy spaces ⋮ Infinitely many solutions for \(p\)-fractional Choquard type equations involving general nonlocal nonlinearities with critical growth via the concentration compactness method ⋮ Calderón–Zygmund theory in Lorentz mixed‐norm spaces and its application to compressible fluids ⋮ Transference and restriction of Fourier multipliers on Orlicz spaces ⋮ Weighted local Hardy spaces with variable exponents ⋮ A dynamic capillarity equation with stochastic forcing on manifolds: A singular limit problem ⋮ The John–Nirenberg inequality for Orlicz–Lorentz spaces in a probabilistic setting ⋮ Characterizations for the difference of weighted composition operators over the polydisk ⋮ Existence of convolution maximizers in \(L_p(\mathbb{R}^n)\) with kernels from Lorentz spaces ⋮ Two-weight dyadic Hardy inequalities ⋮ Interpolation of operators in Hardy-type spaces ⋮ Gradient estimates for a class of higher-order elliptic equations of \(p\)-growth over a nonsmooth domain ⋮ Estimates of the singular set for the Navier-Stokes equations with supercritical assumptions on the pressure ⋮ Self-similar solution for Hardy operator ⋮ Asymptotics of singular values for quantised derivatives on noncommutative tori ⋮ Gagliardo-Nirenberg inequalities in Lorentz type spaces ⋮ A speed preserving Hilbert gradient flow for generalized integral Menger curvature ⋮ Normalized solutions for a fourth-order Schrödinger equation with a positive second-order dispersion coefficient ⋮ Hardy spaces and the Neumann problem in \(L^p\) for elliptic equation with periodic high-contrast coefficients in Lipschitz domains ⋮ Regularity of solutions for nonlocal diffusion equations on periodic distributions ⋮ One-scale H-distributions and variants ⋮ Some applications of \(L^1\)-estimates of fractional integral operators in Lorentz spaces ⋮ Estimate for some integral operators and their commutators on generalized fractional mixed Morrey spaces ⋮ Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum. ⋮ Inequalities in time-frequency analysis ⋮ Discrete restriction estimates for forms in many variables ⋮ Stable singularity formation for the Keller-Segel system in three dimensions ⋮ On the regularity criteria for the three‐dimensional compressible Navier–Stokes system in Lorentz spaces ⋮ Uncertainty principles of the fractional Clifford–Fourier transform ⋮ Nonuniform sampling theorem for non-decaying signals in mixed-norm spaces \(L_{\overrightarrow{p},\frac{1}{\omega}}(\mathbb{R}^d)\) ⋮ A groupoid approach to the Wodzicki residue ⋮ On some operators associated with non-degenerate symmetric \(\alpha \)-stable probability measures ⋮ Transference of bilinear multipliers on Lorentz spaces ⋮ Quasi-classical ground states. I: Linearly coupled Pauli-Fierz Hamiltonians ⋮ Remarks on the linear wave equation ⋮ Generalized localization and summability almost everywhere of multiple Fourier series and integrals ⋮ Well-posedness and stability for a class of fourth-order nonlinear parabolic equations ⋮ Difference of weighted composition operators over the ball ⋮ Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus ⋮ Sharp \(L^p \to L^{q,\infty}\) estimates for the Hilbert transform ⋮ Trigonometric polynomials with frequencies in the set of squares and divisors in a short interval ⋮ On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Rónyai theorem ⋮ Removable singularities for solutions of the fractional heat equation in time varying domains ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Complete boundedness of heat semigroups on the von Neumann algebra of hyperbolic groups ⋮ Sharp subcritical and critical \(L^p\) Hardy inequalities on the sphere ⋮ Nonlinear nonlocal Douglas identity ⋮ Scattering by Finely Layered Obstacles: Frequency-Explicit Bounds and Homogenization ⋮ Bilinear wavelet representation of Calderón-Zygmund forms ⋮ Restricted estimates of the fractional integral on the diagonal ⋮ The composition of singular integral operators with nonsmooth kernels ⋮ Approximation of kernel projection operators in shift-invariant subspaces of function spaces with mixed norms ⋮ New life-span results for the nonlinear heat equation ⋮ A double Fourier sphere method for \(d\)-dimensional manifolds ⋮ Delsarte’s extremal problem and packing on locally compact Abelian groups ⋮ On simulation of continuous determinantal point processes ⋮ Extension domains for Hardy spaces ⋮ Uniform sparse domination and quantitative weighted boundedness for singular integrals and application to the dissipative quasi-geostrophic equation ⋮ Properties of the fractional Clifford–Fourier transform ⋮ Nonuniformly elliptic Schauder theory ⋮ Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds ⋮ Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations ⋮ Weak-type estimate for the Littlewood-Paley operators associated with Laplace-Bessel differential operator ⋮ Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings ⋮ On local smoothing problems and Stein’s maximal spherical means ⋮ Global existence and spatial analyticity for a nonlocal flux with fractional diffusion ⋮ Real interpolation between strong martingale Hardy spaces ⋮ Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications ⋮ Restriction estimates in a conical singular space: Schrödinger equation ⋮ Analysis of a sinc-Galerkin Method for the Fractional Laplacian ⋮ Regularity theory and Green's function for elliptic equations with lower order terms in unbounded domains ⋮ Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model ⋮ Solutions of Navier–Stokes–Maxwell systems in large energy spaces ⋮ Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space ⋮ Projection method for solving equations for multidimensional operators with anisotropically homogeneous kernels of compact type ⋮ Generalized Riesz Transforms, Quasi-Monogenic Functions and Frames ⋮ Some norm inequalities in Musielak-Orlicz spaces ⋮ Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and L-L Fourier multipliers on compact homogeneous manifolds ⋮ Unnamed Item ⋮ On Positivity Preserving, Translation Invariant Operators in $$ \mathit L^p (\mathbb R^n)^m $$ ⋮ The hyper-singular cousin of the Bergman projection ⋮ BOCHNER–RIESZ MEANS ON BLOCK-SOBOLEV SPACES IN COMPACT LIE GROUP ⋮ A Gutzwiller trace formula for large hermitian matrices ⋮ The Vortex Method for Two-Dimensional Ideal Flows in Exterior Domains ⋮ Reproducing kernels of Sobolev spaces on ℝd and applications to embedding constants and tractability ⋮ Functional Identification of Spike-Processing Neural Circuits ⋮ A NOTE ON GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS ⋮ Three-commutators revisited ⋮ Weak type endpoint estimates for the commutators of rough singular integral operators ⋮ WEIGHTED WEAK TYPE ENDPOINT ESTIMATES FOR THE COMPOSITIONS OF CALDERÓN–ZYGMUND OPERATORS ⋮ Scattering theory in homogeneous Sobolev spaces for Schrödinger and wave equations with rough potentials ⋮ Limiting absorption principle on L p-spaces and scattering theory ⋮ An effective equidistribution result for SL(2,R)⋉(R2)⊕k and application to inhomogeneous quadratic forms ⋮ A Thought on Generalized Morrey Spaces ⋮ Calderon's Complex Interpolation of Morrey Spaces ⋮ On the best constant in the estimate related to 𝐻¹-𝐵𝑀𝑂 duality ⋮ Characterization of Function Spaces Using Wavelets ⋮ On estimates for the norms of the Hardy operator acting in the Lorenz spaces ⋮ Automorphic period and the central value of Rankin-Selberg L-function ⋮ Log-Lipschitz embeddings of homogeneous sets with sharp logarithmic exponents and slicing products of balls ⋮ Pointwise convergence of lacunary partial sums of almost periodic Fourier series ⋮ Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance ⋮ On the Hausdorff dimension of Riemann’s non-differentiable function ⋮ Holomorphic function spaces on homogeneous Siegel domains ⋮ Variation of Calderón–Zygmund operators with matrix weight ⋮ Distributions of anisotropic order and applications to H-distributions ⋮ On the boundedness of the Dunkl spherical maximal operator ⋮ Global-in-time solutions to three-dimensional magnetohydrodynamics equations with a class of large initial data ⋮ Green’s function for second order elliptic equations with singular lower order coefficients ⋮ Compactness of the commutators of intrinsic square functions on weighted Lebesgue spaces ⋮ Radial maximal function characterizations for Hardy spaces on RD-spaces ⋮ Fractional integral operators on Morrey spaces built on rearrangement-invariant quasi-Banach function spaces ⋮ A fundamental solution to the time-periodic Stokes equations ⋮ The lattice point counting problem on the Heisenberg groups ⋮ Weak-type estimates and potential estimates for elliptic equations with drift terms ⋮ \(\varepsilon\)-regularity for systems involving non-local, antisymmetric operators ⋮ Non-commutative ergodic averages of balls and spheres over Euclidean spaces ⋮ Effective energy integral functionalsfor thin films on curl-free vector fields in the Orlicz–Sobolev space setting ⋮ Some results for the commutators of generalized Hausdorff operator ⋮ On composition of maximal operator and Bochner-Riesz operator at the critical index ⋮ On the generalized Hardy-Rellich inequalities ⋮ Extensions of Fefferman-Stein maximal inequalities ⋮ Lorentz Estimates for Weak Solutions of Quasi-linear Parabolic Equations with Singular Divergence-free Drifts ⋮ The endpoint Fefferman-Stein inequality for the strong maximal function with respect to nondoubling measure ⋮ A weak-L^p Prodi-Serrin type regularity criterion for a bioconvective flow ⋮ Kolmogorov Equations Associated to the Stochastic Two Dimensional Euler Equations ⋮ Strain-Gradient Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy with Mixed Growth ⋮ A local theory for a fractional reaction-diffusion equation ⋮ Uniform bounds of discrete Birman–Schwinger operators ⋮ Decay estimates and symmetry of finite energy solutions to elliptic systems in \mathbb{R}^n ⋮ Boundary value problems in Lipschitz domains for equations with lower order coefficients ⋮ Degenerate Poincaré–Sobolev inequalities ⋮ An Endpoint Alexandrov Bakelman Pucci Estimate in the Plane ⋮ Unnamed Item ⋮ A Compactness Tool for the Analysis of Nonlocal Evolution Equations ⋮ Generalized $T^p_u$ spaces: On the trail of Calderón and Zygmund ⋮ Unnamed Item ⋮ Fundamental Solutions for Anisotropic Elliptic Equations: Existence and A Priori Estimates ⋮ Compressed Sensing Photoacoustic Tomography Reduces to Compressed Sensing for Undersampled Fourier Measurements ⋮ Weighted norm inequalities for the Opdam–Cherednik transform ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations ⋮ Asymptotics of singular values for quantum derivatives