Analysis and applications: The mathematical work of Elias Stein

DOI10.1090/bull/1691zbMath1452.32001OpenAlexW3009256979WikidataQ112628823 ScholiaQ112628823MaRDI QIDQ5123055

Alex Ionescu, Stephen Wainger, Charles L. Fefferman, Terence C. Tao

Publication date: 25 September 2020

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/bull/1691

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces (42-02)

Related Items

Riesz conjugate functions theorem for harmonic quasiconformal mappings ⋮ On (Fejér-)Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli ⋮ Large deviation principles for stochastic volatility models with reflection ⋮ Fourier restriction estimates on quantum Euclidean spaces ⋮ Conformal and CR mappings on Carnot groups

Cites Work

• COMMUTATORS OF SINGULAR INTEGRAL OPERATORS
• On higher gradients of harmonic functions
• A Maximal Function Characterization of the Class H p
• Sharp L 2 estimates for one-dimensional oscillatory integral operators with C ∞ phase
• ON THE MEAN INVERSION OF FOURIER AND HANKEL TRANSFORMS
• UNIFORMLY BOUNDED REPRESENTATIONS OF GROUPS
• Pointwise convergence of Fourier series
• On multiplier transformations
• Notions of convexity
• Sharp \(L^2\) bounds for oscillatory integral operators with \(C^\infty\) phases
• Two discrete fractional integrals
• A restriction theorem for the Fourier transform
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximal decay inequalities for trilinear oscillatory integrals of convolution type
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Multi-parameter singular Radon transforms. I: The \(L^2\) theory
• Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory
• On the Hardy-Littlewood maximal function for the cube
• Averages in the plane over convex curves and maximal operators
• Estimates for maximal functions associated with hypersurfaces in \(\mathbb R^3\) and related problems of harmonic analysis
• The weak type \((1,1)\) bounds for the maximal function associated to cubes grow to infinity with the dimension
• Discrete fractional Radon transforms and quadratic forms
• The spectrum of the Leray transform for convex Reinhardt domains in \(\mathbb C^2\)
• Multiplier transformations. II
• A geometric bound for maximal functions associated to convex bodies
• Oscillatory integral operators with homogeneous polynomial phases in several variables
• Estimates of kernels on three-dimensional CR manifolds
• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• The (weak-\(L^{2}\)) boundedness of the quadratic Carleson operator
• Hilbert transforms along curves. I: Nilpotent groups
• A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables
• Fundamental solutions for second order subelliptic operators
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• On the maximal ergodic theorem for certain subsets of the integers
• On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets
• Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds
• Estimates for the parametrix of the Kohn Laplacian on certain domains
• Boundary behavior of the Bergman kernel function in \({\mathbb{C}}^ 2\)
• Parabolic invariant theory in complex analysis
• Oscillatory integrals with singular symbols
• Weak type \(L^ 1\) estimates for maximal functions on non-compact symmetric spaces
• Zonal multipliers on the Heisenberg group
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Propagation of singularities and maximal functions in the plane
• Behavior of the Bergman projection on the Diederich-Fornæss worm
• The Kunze-Stein phenomenon
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• \(L^p\)-bounds for spherical maximal operators on \(\mathbb Z^n\)
• A proof of boundedness of the Carleson operator
• An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators
• A nilpotent Roth theorem.
• Square function estimates for discrete Radon transforms
• Polynomial Carleson operators along monomial curves in the plane
• On the \(L^ p\)-bounds for maximal functions associated to convex bodies in \({\mathbb{R}}^ n\)
• Oscillatory integral operators with low-order degeneracies.
• Oscillatory and Fourier integral operators with degenerate canonical relations
• The \(Tb\)-theorem on non-homogeneous spaces.
• The Bochner-Riesz conjecture implies the restriction conjecture
• Maximal polynomial modulations of singular integrals
• Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem
• Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius
• Sparse bounds for the discrete spherical maximal functions
• The discrete spherical averages over a family of sparse sequences
• The proof of the \(l^2\) decoupling conjecture
• A polynomial Carleson operator along the paraboloid
• Rearrangement inequalities on semisimple Lie groups
• On convergence and growth of partial sums of Fourier series
• Inequalities for strongly singular convolution operators
• Convergence almost everywhere of certain singular integrals and multiple Fourier series
• The multiplier problem for the ball
• A note on spherical summation multipliers
• Estimates for singular Radon transforms and pseudodifferential operators with singular symbols
• On maximal Sobolev and Holder estimates for the tangential Cauchy-Riemann operator and boundary Laplacian
• A multi-dimensional resolution of singularities with applications to analysis
• On discrete fractional integral operators and mean values of Weyl sums
• Averages along polynomial sequences in discrete nilpotent groups: singular Radon transforms
• Opérateurs intégraux singuliers sur certaines courbes du plan complexe
• Strictly pseudoconvex domains in 𝐶ⁿ
• $L^p$ boundedness of discrete singular Radon transforms
• Pointwise Estimates for the Relative Fundamental Solution of $\overline{\partial}_b$
• Strong variational and jump inequalities in harmonic analysis
• Uniform estimates for cubic oscillatory integrals
• An almost-orthogonality principle with applications to maximal functions associated to convex bodies
• On High Dimensional Maximal Functions Associated to Convex Bodies
• Regularity Properties of the ∂ b Equation on Weakly Pseudoconvex CR Manifolds of Dimension 3
• The Strong Maximal Function on a Nilpotent Group
• On Hilbert transforms along curves
• A maximal function associated to the curve ( t, t ² )
• On Hilbert Transforms Along Curves. II
• Cauchy integrals on Lipschitz curves and related operators
• L 2 Boundedness of Hilbert Transforms Along Surfaces and Convolution Operators Homogeneous with Respect to a Multiple Parameter Group
• On integral representations for the Neumann operator
• Radon transforms and finite type conditions
• Multidimensional van der Corput and sublevel set estimates
• An endpoint estimate for the discrete spherical maximal function
• Dimension free bounds for the Hardy–Littlewood maximal operator associated to convex sets
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• On Fourier coefficients and transforms of functions of two variables
• 𝐿^{𝑝} improving bounds for averages along curves
• Estimates for maximal functions associated to hypersurfaces in $\mathbb {R}^3$ with height $h<2$: Part I