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