English

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

Classical Analysis and ODEs 2019-11-05 v2 Functional Analysis

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 Rd\mathbb R^d and Zd\mathbb Z^d.

Keywords

Cite

@article{arxiv.1812.00153,
  title  = {On the Hardy--Littlewood maximal functions in high dimensions: Continuous and discrete perspective},
  author = {Jean Bourgain and Mariusz Mirek and Elias M. Stein and Błażej Wróbel},
  journal= {arXiv preprint arXiv:1812.00153},
  year   = {2019}
}

Comments

24 pages, no figures. Dedicated to Fulvio Ricci on the occasion of his 70th birthday. Revised following the referee report