Operator-valued Fourier multiplier theorems and maximal $L_p$-regularity

DOI10.1007/PL00004457zbMath0989.47025OpenAlexW2080951455MaRDI QIDQ5947416

Publication date: 16 October 2001

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/pl00004457

zbMATH Keywords

Hilbert transform $R$-boundedness bounded analytic semigroup of operators Bourgain linking Fourier multiplier Littlewood-Paley type square functions maximal $L^p$ regularity Mihlin multiplier theorem Rademacher function UMD property UMD spaces

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Linear operators on function spaces (general) (47B38)

Related Items

Well-posedness of second order evolution equation on discrete time ⋮ Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions ⋮ Stochastic evolution equations driven by Liouville fractional Brownian motion ⋮ On the well-posedness of degenerate fractional differential equations in vector valued function spaces ⋮ Periodic solutions of third-order degenerate differential equations in vector-valued functional spaces ⋮ $H^\infty $-calculus for submarkovian generators ⋮ Energy equality and uniqueness of weak solutions of a ``viscous incompressible fluid $+$ rigid body system with Navier slip-with-friction conditions in a 2D bounded domain ⋮ Periodic solutions of integro-differential equations in vector-valued function spaces ⋮ ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS INL^P([0,T;E) SPACES] ⋮ On the global well-posedness for the compressible Navier-Stokes equations with slip boundary condition ⋮ The Lp-regularity properties of nonlocal wave equations and applications ⋮ R-sectoriality of Cylindrical Boundary Value Problems ⋮ Weak Neumann implies Stokes ⋮ Optimal $L^{p}$- $L^{q}$-estimates for parabolic boundary value problems with inhomogeneous data ⋮ lp-maximal regularity for fractional difference equations on UMD spaces ⋮ A refinement of Baillon’s theorem on maximal regularity ⋮ Linear and nonlinear degenerate boundary value problems in Besov spaces ⋮ Dimension free boundedness of Riesz transforms for the Grushin operator ⋮ On the structure of semigroups on L_p with a bounded H^∞ -calculus ⋮ Global bifurcation of periodic solutions in nonlinear evolution problems with periodic forcing ⋮ Nonlinear abstract boundary value problems modelling atmospheric dispersion of pollutants ⋮ Obituary: Nigel John Kalton, 1946-2010 ⋮ Discrete almost maximal regularity and stability for fractional differential equations in $L^p([0, 1, \Omega)$] ⋮ Maximal regularity of second-order evolution equations with infinite delay in Banach spaces ⋮ Periodic solutions of third-order integro-differential equations in vector-valued functional spaces ⋮ THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS ⋮ On the maximal $L_p$-$L_q$ regularity theorem for the linearized electro-magnetic field equations with interface conditions ⋮ On the Stokes system in cylindrical domains ⋮ Existence and uniqueness of solutions for a class of discrete-time fractional equations of order $2<\alpha \leq 3$ ⋮ Bounded invertibility and separability of a parabolic type singular operator in the space L2(R2) ⋮ A-Stable Time Discretizations Preserve Maximal Parabolic Regularity ⋮ On joint functional calculus for Ritt operators ⋮ Well-posedness of differential equations on $B^s_{p, q}(\mathbb{R}; X)$ and $F^s_{p, q}(\mathbb{R}; X)$ ⋮ ON R-SECTORIAL DERIVATIVES ON BERGMAN SPACES ⋮ Two-weight $L^{p}$-inequalities for dyadic shifts and the dyadic square function ⋮ Maximal $L^p$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra ⋮ Maximal Regularity of Fully Discrete Finite Element Solutions of Parabolic Equations ⋮ Elliptic Differential-Operator Problems with the Spectral Parameter in Both the Equation and Boundary Conditions and the Corresponding Abstract Parabolic Initial Boundary Value Problems ⋮ EXISTENCE AND MAXIMAL REGULARITY OF SOLUTIONS IN L_2(R^2) FOR A HYPERBOLIC TYPE DIFFERENTIAL EQUATION WITH QUICKLY GROWING COEFFICIENTS ⋮ Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations ⋮ Singular degenerate problems occurring in biosorption process ⋮ Optimal regular differential operators with variable coefficients and applications ⋮ A Maximal Regularity Approach to the Analysis of Some Particulate Flows ⋮ A perturbation result for semi-linear stochastic differential equations in UMD Banach spaces ⋮ Convergence of subdiagonal Padé approximations of $C _{0}$-semigroups ⋮ $L^p$-maximal regularity of degenerate delay equations with periodic conditions ⋮ Banach-valued multilinear singular integrals ⋮ UMD Banach spaces and the maximal regularity for the square root of several operators ⋮ Global solution of nonlinear stochastic heat equation with solutions in a Hilbert manifold ⋮ Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation ⋮ On a maximal $L_p - L_q$ approach to the compressible viscous fluid flow with slip boundary condition ⋮ The Global Well-Posedness for the Compressible Fluid Model of Korteweg Type ⋮ Analysis of Viscous Fluid Flows: An Approach by Evolution Equations ⋮ ℛ $${\mathcal R}$$ Boundedness, Maximal Regularity and Free Boundary Problems for the Navier Stokes Equations ⋮ Perturbation theory, stability, boundedness and asymptotic behaviour for second order evolution equation in discrete time ⋮ Fourier multipliers in Banach function spaces with UMD concavifications ⋮ The Stokes operator in weighted $L^q$-spaces. II: Weighted resolvent estimates and maximal $L^p$-regularity ⋮ Fractional differential operators in vector-valued spaces and applications ⋮ Some Free Boundary Problem for Two-Phase Inhomogeneous Incompressible Flows ⋮ Complex powers for cone differential operators and the heat equation on manifolds with conical singularities ⋮ $\mathcal R$-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators ⋮ Vector-valued multiparameter singular integrals and pseudodifferential operators ⋮ Degenerate differential operators with parameters ⋮ Kato's square root problem in Banach spaces ⋮ Separable anisotropic differential operators in weighted abstract spaces and applications ⋮ Unnamed Item ⋮ Analytic solutions of Volterra equations via semigroups ⋮ Operator-valued multiplier theorems characterizing Hilbert spaces ⋮ A note on discrete maximal regularity for functional difference equations with infinite delay ⋮ An operator-valued $Tb$ theorem ⋮ Maximal B-regular boundary value problems with parameters ⋮ On singular integral and martingale transforms ⋮ $L^q$ estimates of weak solutions to the stationary Stokes equations around a rotating body ⋮ Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra ⋮ Pseudodifferential operators on Bochner spaces and an application ⋮ Unnamed Item ⋮ Maximal regularity: Positive counterexamples on UMD-Banach lattices and exact intervals for the negative solution of the extrapolation problem ⋮ Embedding and maximal regular differential operators in Sobolev--Lions spaces ⋮ 𝐿^{𝑝}-𝐿^{𝑞} maximal regularity for some operators associated with linearized incompressible fluid-rigid body problems ⋮ Calderón-Zygmund operators with operator-valued kernel on homogeneous Besov spaces ⋮ A perturbation theory for the discrete harmonic oscillator equation ⋮ Maximal $L_p$-regularity of non-local boundary value problems ⋮ The Work of Yoshihiro Shibata ⋮ Global well-posedness for free boundary problem of the Oldroyd-B model fluid flow ⋮ A characterization of periodic solutions for time-fractional differential equations in UMD spaces and applications ⋮ Existence and uniqueness of solutions of the fractional integro-differential equations in vector-valued function space ⋮ On Strong Dynamics of Compressible Two-Component Mixture Flow ⋮ Existence and maximalL^p-regularity of solutions for the porous medium equation on manifolds with conical singularities ⋮ Discrete maximal regularity for abstract Cauchy problems ⋮ NEW COUNTEREXAMPLES ON RITT OPERATORS, SECTORIAL OPERATORS AND -BOUNDEDNESS ⋮ Embedding of vector-valued Morrey spaces and separable differential operators ⋮ $H^\infty$-calculus for products of non-commuting operators ⋮ Square functions and $H^\infty$ calculus on subspaces of $L^p$ and on Hardy spaces ⋮ $L^p$-maximal regularity for second order Cauchy problems ⋮ On operator-valued Fourier multiplier theorems ⋮ Unnamed Item ⋮ Operator-valued Fourier multipliers on periodic Triebel spaces ⋮ An Extension Problem and Hardy Type Inequalities for the Grushin Operator ⋮ A T1 theorem for integral transformations with operator-valued kernel ⋮ About Compressible Viscous Fluid Flow in a 2-dimensional Exterior Domain ⋮ Riesz transforms and multipliers for the Bessel-Grushin operator ⋮ Global well posedness for a Q-tensor model of nematic liquid crystals ⋮ Reacting multi-component fluids: regular solutions in Lorentz spaces ⋮ Maximal regularity for compressible two-fluid system ⋮ End-point maximal $L^1$-regularity for the Cauchy problem to a parabolic equation with variable coefficients ⋮ Operator-valued dyadic shifts and the $T(1)$ theorem ⋮ Nonlocal problems for Boussinesq equations ⋮ On the free boundary problem for the Oldroyd-B model in the maximal $L_p-L_q$ regularity class ⋮ Abstract differential equations with VMO coefficients in half space and applications ⋮ A transference principle for general groups and functional calculus on UMD spaces ⋮ Stokes equations with small parameters in half plane ⋮ Linear and nonlinear abstract differential equations of high order ⋮ Maximal regularity and Hardy spaces ⋮ End-point maximal regularity and its application to two-dimensional Keller-Segel system ⋮ Global strong solutions for a class of heterogeneous catalysis models ⋮ Periodic solutions of second order differential equations in Banach spaces ⋮ Abstract elliptic equations with integral boundary conditions ⋮ Fourier multipliers and periodic solutions of delay equations in Banach spaces ⋮ Operator-valued Fourier Haar multipliers ⋮ $L^{p}(\mu) \to L^{q}(\nu)$ characterization for well localized operators ⋮ Weighted norm inequalities, off-diagonal estimates and elliptic operators. III: Harmonic analysis of elliptic operators ⋮ Hölder continuous solutions for integro-differential equations and maximal regularity ⋮ A conserved phase field system with memory and relaxed chemical potential ⋮ Riesz transforms and multipliers for the Grushin operator ⋮ On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain ⋮ On pressure stabilization method for nonstationary Navier-Stokes equations ⋮ R-bounded approximating sequences and applications to semigroups ⋮ Second order equations in functional spaces: qualitative and discrete well-posedness ⋮ $\mathcal {R}$-sectoriality of higher-order elliptic systems on general bounded domains ⋮ Regularity of semigroups via the asymptotic behaviour at zero ⋮ Pathwise Hölder convergence of the implicit-linear Euler scheme for semi-linear SPDEs with multiplicative noise ⋮ $L^{p}$-theory for some elliptic and parabolic problems with first order degeneracy at the boundary ⋮ Nonlinear abstract boundary-value problems in vector-valued function spaces and applications ⋮ Fourier decomposition of properly elliptic boundary value problems in a half-plane ⋮ Maximal regular abstract elliptic equations and applications ⋮ Maximal regular boundary value problems in Banach-valued function spaces and applications ⋮ Concentration and universal randomisation of proper subspaces ⋮ Linear and nonlinear abstract elliptic equations with $VMO$ coefficients and applications ⋮ Pseudodifferential operators with non-regular operator-valued symbols ⋮ Nonlocal Navier-Stokes problems in abstract function spaces and applications ⋮ Embedding operators in vector-valued weighted Besov spaces and applications ⋮ Linear first-order evolution problems without initial conditions ⋮ Second order elliptic differential-operator equations with unbounded operator boundary conditions in $UMD$ Banach spaces ⋮ Projections onto convex sets and $L ^{p }$-quasi-contractivity of semigroups ⋮ The instationary Stokes equations in weighted Bessel-potential spaces ⋮ Functional calculus and square functions in noncommutative $L^{p}$-spaces. ⋮ On the maximal $L_{p}$-$L_{q}$ regularity of the Stokes problem with first order boundary condition; model problems ⋮ Embeddings and separable differential operators in spaces of Sobolev-lions type ⋮ Regular degenerate separable differential operators and applications ⋮ Operator-valued Fourier multiplier theorems on $L_{p}$($X$) and geometry of Banach spaces. ⋮ Singular perturbation degenerate problems occurring in atmospheric dispersion of pollutants ⋮ Well-posedness of fractional differential equations on vector-valued function spaces ⋮ Littlewood-Paley-Stein theory for semigroups in UMD spaces ⋮ Separable anisotropic elliptic operators and applications ⋮ On some free boundary problem for a compressible barotropic viscous fluid flow ⋮ Uniform separable differential operators with parameters ⋮ Abstract elliptic operators appearing in atmospheric dispersion ⋮ Periodic solutions of fractional differential equations with delay ⋮ Approximating the coefficients in semilinear stochastic partial differential equations ⋮ Traces and embeddings of anisotropic function spaces ⋮ Stokes operators with variable coefficients and applications ⋮ The Kalton-Lancien theorem revisited: maximal regularity does not extrapolate ⋮ On the $\mathcal{R}$-boundedness for the two phase problem: compressible-incompressible model problem ⋮ $L_p$-$L_q$ maximal regularity and viscous incompressible flows with free surface ⋮ Semilinear evolution equations of second order via maximal regularity ⋮ Stochastic evolution equations in UMD Banach spaces ⋮ Maximum-norm stability and maximal $L^p$ regularity of FEMs for parabolic equations with Lipschitz continuous coefficients ⋮ Difference norms for vector-valued Bessel potential spaces with an application to pointwise multipliers ⋮ Dunkl spectral multipliers with values in UMD lattices ⋮ Maximal regularity for perturbed integral equations on periodic Lebesgue spaces ⋮ Maximal regularity for non-autonomous equations with measurable dependence on time ⋮ On maximal regularity of type $L^p-L^q$ under minimal assumptions for elliptic non-divergence operators ⋮ Maximal regularity for non-autonomous Schrödinger type equations ⋮ Degenerate anisotropic differential operators and applications ⋮ Maximal regularity for flexible structural systems in Lebesgue spaces ⋮ Maximal $L_{p}-L_{q}$ regularity of the linearized initial-boundary value problem for motion of compressible viscous fluids ⋮ Maximal $L_{p}$-$L_{q}$ regularity for the two-phase Stokes equations; model problems ⋮ Singular convolution integrals with operator-valued kernel ⋮ Mild well-posedness of vector-valued problems on the real line ⋮ $\gamma $-bounded representations of amenable groups ⋮ Linear and nonlinear abstract equations with parameters ⋮ Anisotropic Fourier multipliers and singular integrals for vector-valued functions ⋮ On maximal parabolic regularity for non-autonomous parabolic operators ⋮ Regular boundary value problems for complete second order elliptic differential-operator equations in $UMD$ Banach spaces ⋮ A stochastic Datko-Pazy theorem ⋮ Pointwise convergence for semigroups in vector-valued $L^{p}$ spaces ⋮ Free boundary value problems for abstract elliptic equations and applications ⋮ Analytic semigroups of pseudodifferential operators on vector-valued Sobolev spaces ⋮ B-separable boundary value problems in Banach-valued function spaces ⋮ On maximal $L^p$-regularity ⋮ Maximal regularity of the discrete harmonic oscillator equation ⋮ Inhomogeneous symbols, the Newton polygon, and maximal $L^p$-regularity ⋮ Semilinear evolution equations on discrete time and maximal regularity ⋮ On semi-$R$-boundedness and its applications ⋮ Multipoint problems for degenerate abstract differential equations ⋮ Weighted estimates for operator-valued Fourier multipliers ⋮ Nonlocal fractional differential equations and applications ⋮ Regularity properties of degenerate convolution-elliptic equations ⋮ Linear and nonlinear degenerate abstract differential equations with small parameter ⋮ On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface ⋮ On the $${\mathscr {R}}$$ R -Bounded Solution Operator and the Maximal $$L_p$$ L p - $$L_q$$ L q Regularity of the Stokes Equations With Free Boundary Condition ⋮ On the L_p–L_q maximal regularity for the linear thermoelastic plate equation in a bounded domain ⋮ The maximal regularity property of abstract integrodifferential equations ⋮ Isometric dilations and 𝐻^{∞} calculus for bounded analytic semigroups and Ritt operators ⋮ Periodic solutions of second‐order degenerate differential equations with infinite delay in Banach spaces ⋮ Maximal regularity of parabolic equations associated with a discrete Laplacian ⋮ Maximal $L^p$-regularity and $H^\infty$-calculus for block operator matrices and applications ⋮ Off-diagonal bounds for the Dirichlet-to-Neumann operator on Lipschitz domains ⋮ Nonlocal fractional elliptic equations and applications ⋮ Strongly $L^p$ well-posedness for abstract time-fractional Moore-Gibson-Thompson type equations ⋮ Periodic $\mathrm{L}_p$ estimates by $\mathscr{R}$-boundedness: applications to the Navier-Stokes equations ⋮ Maximal regularity for the Cauchy problem of the heat equation in BMO ⋮ Motion of rigid bodies of arbitrary shape in a viscous incompressible fluid: wellposedness and large time behaviour ⋮ Wellposedness of second order evolution equations ⋮ Boundedness and weak stabilization in a degenerate chemotaxis model arising from tumor invasion ⋮ $L_p$-maximal regularity for parabolic and elliptic boundary value problems with boundary conditions of mixed differentiability orders ⋮ Logarithmic Stable Recovery of the Source and the Initial State of Time Fractional Diffusion Equations ⋮ Linear and quasilinear evolution equations in the context of weighted $L_p$-spaces ⋮ $L^s(L^q)$-estimates of the pressure -- the proof of Sohr-von Wahl and its impact on mathematical fluid dynamics ⋮ Well‐posedness of second‐order degenerate differential equations with finite delay on Lp(ℝ;X)$$ {L}^p\left(\mathbb{R};X\right) $$ ⋮ Separable differential operators with parameters ⋮ Euclidean Structures and Operator Theory in Banach Spaces ⋮ On Maximal Regularity Estimates for Discontinuous Galerkin Time-Discrete Methods ⋮ An optimal multiplier theorem for Grushin operators in the plane. I ⋮ Maximal regularity and two‐sided estimates of the approximation numbers of the nonlinear Sturm–Liouville equation solutions with rapidly oscillating coefficients in L₂(ℝ) ⋮ Homogeneous Sobolev global-in-time maximal regularity and related trace estimates ⋮ Analyticity and discrete maximal regularity on $\ell_p$-spaces ⋮ Maximal regularity of second order delay equations in Banach spaces ⋮ Rademacher bounded families of operators on 𝐿₁ ⋮ Maximal regularity of discrete second order Cauchy problems in Banach spaces ⋮ On Well-Posedness of Difference Schemes for Abstract Elliptic Problems in L^p([0, T;E) Spaces] ⋮ Irregular boundary value problems for second order elliptic differential-operator equations in UMD Banach spaces ⋮ On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain ⋮ Linear and nonlinear nonlocal boundary value problems for differential-operator equations ⋮ Space-Time Regularity of Solutions of the Parabolic Stochastic Cauchy Problem ⋮ On the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer ⋮ Maximal regularity in $l_{p}$ spaces for discrete time fractional shifted equations ⋮ A posteriori error estimates for Radau IIA methods via maximal parabolic regularity ⋮ Regularity properties of nonlocal fractional differential equations and applications ⋮ Maximal $L^p-L^q$ regularity for two-phase fluid motion in the linearized Oberbeck-Boussinesq approximation ⋮ Maximal $L^1$-regularity for parabolic initial-boundary value problems with inhomogeneous data ⋮ Maximal regularity of second-order equations with delay ⋮ New thought on Matsumura-Nishida theory in the $L_p$-$L_q$ Maximal regularity framework ⋮ Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of $p$-growth ⋮ Maximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations ⋮ Time-frequency analysis of the Dirac equation ⋮ The Navier-Stokes equations in exterior Lipschitz domains: $L^p$-theory ⋮ The semigroup generated by the Dirichlet Laplacian of fractional order ⋮ Bilinear embedding for divergence-form operators with complex coefficients on irregular domains ⋮ A sharp equivalence between $H ^{\infty }$ functional calculus and square function estimates ⋮ The $\mathcal{R}$-bounded operator families arising from the study of the barotropic compressible flows with free surface ⋮ Multilinear operator-valued Calderón-Zygmund theory ⋮ Discrete maximal regularity of time-stepping schemes for fractional evolution equations ⋮ Maximal $L^1$-regularity for parabolic boundary value problems with inhomogeneous data in the half-space ⋮ An explicit counterexample for the $L^p$-maximal regularity problem ⋮ The Laplacian on cylindrical domains ⋮ Multilinear singular integrals on non-commutative $L^p$ spaces ⋮ Periodic solutions of second order degenerate differential equations with finite delay in Banach spaces ⋮ Solutions of second-order degenerate integro-differential equations in vector-valued function spaces ⋮ The periodic version of the Da Prato-Grisvard theorem and applications to the bidomain equations with FitzHugh-Nagumo transport ⋮ Lebesgue regularity for nonlocal time-discrete equations with delays ⋮ Second order optimality conditions for optimal control of quasilinear parabolic equations ⋮ Weighted norm inequalities for Weyl multipliers and Fourier multipliers on the Heisenberg group ⋮ Singular limit for the magnetohydrodynamics of the damped wave type in the critical Fourier-Sobolev space ⋮ Well-posedness for degenerate third order equations with delay and applications to inverse problems ⋮ An operator-valued $T(1)$ theorem for symmetric singular integrals in UMD spaces ⋮ Optimal Sobolev regularity for the Stokes equations on a 2D wedge domain ⋮ Regularity estimates for the Cauchy problem to a parabolic equation associated to fractional harmonic oscillators ⋮ On continuity of solutions for parabolic control systems and input-to-state stability ⋮ $H^{\infty}$-calculus for semigroup generators on BMO ⋮ Maximal regularity of parabolic equations associated to generalized Hardy operators in weighted mixed-norm spaces ⋮ $L^p$ theory for the interaction between the incompressible Navier-Stokes system and a damped plate ⋮ Compressible Navier-Stokes system on a moving domain in the $L_p - L_q$ framework ⋮ Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion ⋮ Discrete maximal regularity and the finite element method for parabolic equations ⋮ Besov and Triebel-Lizorkin spaces for Schrödinger operators with inverse-square potentials and applications ⋮ Strong solutions to compressible-incompressible two-phase flows with phase transitions ⋮ Solvability of initial boundary value problems for non-autonomous evolution equations ⋮ Maximal regularity with weights for parabolic problems with inhomogeneous boundary conditions ⋮ On the maximal regularity for perturbed autonomous and non-autonomous evolution equations ⋮ Fourier multiplier theorems involving type and cotype ⋮ Nonautonomous maximal $L^p$-regularity under fractional Sobolev regularity in time ⋮ Well posedness for semidiscrete fractional Cauchy problems with finite delay ⋮ Quasilinear evolution equations in $L_\mu^P$-spaces with lower regular initial data ⋮ Bounded $H_\infty$-calculus for cone differential operators ⋮ Parameter-dependent Stokes problems in vector-valued spaces and applications ⋮ Linear and nonlinear convolution elliptic equations ⋮ Strong solutions of a neutral type equation with finite delay ⋮ Local strong solutions for the non-linear thermoelastic plate equation on rectangular domains in $L^p$-spaces ⋮ Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in the Hermite setting ⋮ Anisotropic differential operators with parameters and applications ⋮ Stability properties of stochastic maximal $L^p$-regularity ⋮ Maximal regularity of evolution equations on discrete time scales ⋮ Nonlocal Navier-Stokes problem with a small parameter ⋮ Fractional abstract differential equations and applications ⋮ Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation ⋮ Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity ⋮ Stability theory for semigroups using $(L^{p},L^{q})$ Fourier multipliers ⋮ Expanding solutions of quasilinear parabolic equations ⋮ Spatial asymptotics of mild solutions to the time-dependent Oseen system ⋮ The Cauchy problem for Boussinesq equations with general elliptic part ⋮ On the maximal $L_{p}-L_{q}$ regularity of solutions to a general linear parabolic system ⋮ The 3D time-dependent Oseen system: link between $L^p$-integrability in time and pointwise decay in space of the velocity ⋮ Compressible-incompressible two-phase flows with phase transition: model problem ⋮ Well-posedness of third order degenerate differential equations with finite delay in Banach spaces ⋮ Bounded $H_\infty$-calculus for boundary value problems on manifolds with conical singularities ⋮ Maximal $L_p$-$L_q$ regularity for the quasi-steady elliptic problems ⋮ Boundary value problems of elliptic and parabolic type with boundary data of negative regularity ⋮ Operator-valued Fourier-Haar multipliers on vector-valued ${L^1}$ spaces. II: A characterisation of finite dimensionality ⋮ On pointwise $\ell^r$-sparse domination in a space of homogeneous type ⋮ Solvability of the abstract evolution equations in $L^s$-spaces with critical temporal weights ⋮ Stochastic maximal regularity for rough time-dependent problems ⋮ $L^p$-maximal regularity for a class of degenerate integro-differential equations with infinite delay in Banach spaces ⋮ $L^p$-strong solution to fluid-rigid body interaction system with Navier slip boundary condition ⋮ Maximal $L^1$-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space ⋮ On periodic solutions for one-phase and two-phase problems of the Navier-Stokes equations ⋮ $\mathrm{L}^p$-extrapolation of non-local operators: maximal regularity of elliptic integrodifferential operators with measurable coefficients ⋮ The hydrostatic approximation for the primitive equations by the scaled Navier-Stokes equations under the no-slip boundary condition ⋮ Resolvent estimates for a compressible fluid model of Korteweg type and their application ⋮ On the $\mathrm{L}^p$-theory for second-order elliptic operators in divergence form with complex coefficients ⋮ Coercive boundary value problems for regular degenerate differential-operator equations ⋮ Mapping properties of operator-valued pseudo-differential operators ⋮ The Swift-Hohenberg equation on conic manifolds ⋮ Separability properties of singular degenerate abstract differential operators and applications ⋮ The Navier-Stokes equations with the Neumann boundary condition in an infinite cylinder ⋮ Generation of semigroups for the thermoelastic plate equation with free boundary conditions ⋮ The Stokes operator in two-dimensional bounded Lipschitz domains ⋮ Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier-Stokes equations ⋮ Local-in-time existence of strong solutions to a class of the compressible non-Newtonian Navier-Stokes equations ⋮ Elliptic and parabolic boundary value problems in weighted function spaces ⋮ On some free boundary problem of the Navier-Stokes equations in the maximal $L_p - L_q$ regularity class ⋮ A structurally damped plate equation with Dirichlet-Neumann boundary conditions ⋮ Operator-valued $(L^p, L^q)$ Fourier multipliers and stability theory for evolution equations ⋮ Maximal $\gamma$-regularity ⋮ The fractional porous medium equation on manifolds with conical singularities. I ⋮ Staffans-Weiss perturbations for maximal $L^p$-regularity in Banach spaces

This page was built for publication: Operator-valued Fourier multiplier theorems and maximal $L_p$-regularity

Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity