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arXiv · 1812.00154

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

Jean Bourgain·Mariusz Mirek·Elias M. Stein Błażej Wróbel
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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 $p\in[2, \infty]$.

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Jean Bourgain, Mariusz Mirek, Elias M. Stein Błażej Wróbel. 2018-12-01. On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates. https://arxiv.org/abs/1812.00154

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