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

2022/11/21 by Kosz, Dariusz, Rey, Guillermo, Roncal, Luz
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.11641

Abstract

We prove necessary and sufficient conditions for the weak-L^p boundedness, for p ∈ (1,∞), 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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