Dimension-free estimates on $l^2({\mathbb{Z}}^d)$ for discrete dyadic maximal function over $l^1$ balls: small scales

Abstract

We give a dimension-free bound on $l^p({\mathbb{Z}}^d)$ for discrete Hardy-Littlewood operator over $l^1$ balls in ${\mathbb{Z}}^d$ with small dyadic radii, where $p\in [2,\infty ]$.

13 pages, no figures. This is the revised version, incorporating suggestions and simplification from the referees reports. Accepted by the journal Colloquium Mathematicum