Dimension-free estimates on $l^2 (\mathbb Z ^d)$ for a discrete dyadic maximal function over $l^1$ balls: small scales
Volume 175 / 2024
Colloquium Mathematicum 175 (2024), 37-54
MSC: Primary 42B15; Secondary 42B25
DOI: 10.4064/cm9276-12-2023
Published online: 24 January 2024
Abstract
We give a dimension-free bound on $l^p(\mathbb Z ^d)$ for the discrete Hardy–Littlewood operator over the $l^1$ balls in $\mathbb Z ^d$ with small dyadic radii, where $p \in [2, \infty ]$.
