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arXiv · 2211.11641

Weak-type maximal function estimates on the infinite-dimensional torus

Dariusz Kosz·Guillermo Rey·Luz Roncal
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Abstract

We prove necessary and sufficient conditions for the weak-$L^p$ boundedness, for $p \in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality enjoyed by the strong maximal function in dimension two. Our results are quantitatively sharp.

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Dariusz Kosz, Guillermo Rey, Luz Roncal. 2022-11-21. Weak-type maximal function estimates on the infinite-dimensional torus. https://arxiv.org/abs/2211.11641

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