Some remarks on dimension-free estimates for the discrete Hardy-Littlewood maximal functions

DOI10.1007/s11856-022-2382-7zbMath1521.42017arXiv2010.07379MaRDI QIDQ6161726

Dariusz Kosz, Paweł Plewa, Błażej Wróbel, Mariusz Mirek

Publication date: 5 June 2023

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.07379

zbMATH Keywords

sequence spacesHardy-Littlewood maximal functionconvex symmetric bodiesdimension-free estimates

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Discrete version of topics in analysis (39A12)

Related Items (2)

On the solution of Waring problem with a multiplicative error term: Dimension-free estimates ⋮ Dimension-free estimates for Hardy-Littlewood maximal functions with mixed homogeneities

Cites Work

• On the Hardy-Littlewood maximal function for the cube
• The weak type \((1,1)\) bounds for the maximal function associated to cubes grow to infinity with the dimension
• A geometric bound for maximal functions associated to convex bodies
• Maximal inequality for high-dimensional cubes
• The best constant for the centered Hardy-Littlewood maximal inequality
• On the \(L^ p\)-bounds for maximal functions associated to convex bodies in \({\mathbb{R}}^ n\)
• Lower bounds for the weak type \((1, 1)\) estimate for the maximal function associated to cubes in high dimensions
• The development of square functions in the work of A. Zygmund
• An almost-orthogonality principle with applications to maximal functions associated to convex bodies
• On High Dimensional Maximal Functions Associated to Convex Bodies
• Dimension free bounds for the Hardy–Littlewood maximal operator associated to convex sets
• On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective
• 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)

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