On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective
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Publication:5016422
DOI10.1007/978-3-030-72058-2_3zbMath1479.42046arXiv1812.00153OpenAlexW2902576419MaRDI QIDQ5016422
Błażej Wróbel, Mariusz Mirek, Elias M. Stein, Jean Bourgain
Publication date: 13 December 2021
Published in: Geometric Aspects of Harmonic Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.00153
Fourier multipliersconvex bodiesoscillatory integralsHardy-Littlewood maximal functionsdimension-free estimates
Maximal functions, Littlewood-Paley theory (42B25) Multipliers for harmonic analysis in several variables (42B15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
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Cites Work
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- On the Hardy-Littlewood maximal function for the cube
- Averages in the plane over convex curves and maximal operators
- The weak type \((1,1)\) bounds for the maximal function associated to cubes grow to infinity with the dimension
- Estimates for the square variation of partial sums of Fourier series and their rearrangements
- Harmonic analysis on semigroups
- Behavior of maximal functions in \(R^ n\) for large n
- A geometric bound for maximal functions associated to convex bodies
- On convex perturbations with a bounded isotropic constant
- Random martingales and localization of maximal inequalities
- Maximal inequality for high-dimensional cubes
- Maximal and singular integral operators via Fourier transform estimates
- Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
- Holomorphic semi-groups and the geometry of Banach spaces
- On dimension-free variational inequalities for averaging operators in \({\mathbb{R}^d}\)
- On the \(L^ p\)-bounds for maximal functions associated to convex bodies in \({\mathbb{R}}^ n\)
- Jump inequalities via real interpolation
- A bootstrapping approach to jump inequalities and their applications
- Jump inequalities for translation-invariant operators of Radon type on \(\mathbb{Z}^d\)
- \(\ell ^p\left(\mathbb {Z}^d\right)\)-estimates for discrete operators of Radon type: variational estimates
- Lower bounds for the weak type \((1, 1)\) estimate for the maximal function associated to cubes in high dimensions
- Discrete maximal functions in higher dimensions and applications to ergodic theory
- The development of square functions in the work of A. Zygmund
- Some results in harmonic analysis in 𝐑ⁿ, for 𝐧→∞
- An almost-orthogonality principle with applications to maximal functions associated to convex bodies
- On High Dimensional Maximal Functions Associated to Convex Bodies
- Maximal functions: Spherical means
- Differentiation in lacunary directions
- Dimension free bounds for the Hardy–Littlewood maximal operator associated to convex sets
- On Discrete Hardy–Littlewood Maximal Functions over the Balls in $${\boldsymbol {\mathbb {Z}^d}}$$ : Dimension-Free Estimates
- Dimension-Free Estimates for Discrete Hardy-Littlewood Averaging Operators Over the Cubes in ℤd
- Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
