On the Hardy--Littlewood maximal functions in high dimensions: Continuous and discrete perspective

2018/12/01 by Bourgain, Jean, Mirek, Mariusz, Stein, Elias M. +1 · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1812.00153

Abstract

This is a survey article about recent developments in dimension-free estimates for maximal functions corresponding to the Hardy--Littlewood averaging operators associated with convex symmetric bodies in \mathbb R^d and \mathbb Z^d.

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• On high dimensional maximal functions associated to Gaussians, balls, and spheres
• Dimension-free estimates for semi-commutative discrete Hardy-Littlewood maximal operators

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