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

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 $p\in [2,\infty ]$.

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