On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates

Jean Bourgain; Mariusz Mirek; Elias M. Stein Błażej Wróbel

On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates

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

Authors: Jean Bourgain , Mariusz Mirek , Elias M. Stein Błażej Wróbel

Abstract

We show that the discrete Hardy-Littlewood maximal functions associated with the Euclidean balls in $\mathbb Z^d$ with dyadic radii have bounds independent of the dimension on $\ell^p(\mathbb Z^d)$ for $p\in[2, \infty]$ .

Keywords

discrete maximal function hardy-littlewood euclidean balls dimension-free bounds integer lattices

Cite

@article{arxiv.1812.00154,
  title  = {On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates},
  author = {Jean Bourgain and Mariusz Mirek and Elias M. Stein Błażej Wróbel},
  journal= {arXiv preprint arXiv:1812.00154},
  year   = {2019}
}

Comments

25 pages, no figures. Revised following the referee report. To appear in the Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2017-2019, Lecture Notes in Mathematics 2256

On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates

Abstract

Keywords

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