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