English

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

Classical Analysis and ODEs 2023-03-07 v2

Abstract

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

Keywords

Cite

@article{arxiv.2211.11641,
  title  = {Weak-type maximal function estimates on the infinite-dimensional torus},
  author = {Dariusz Kosz and Guillermo Rey and Luz Roncal},
  journal= {arXiv preprint arXiv:2211.11641},
  year   = {2023}
}
R2 v1 2026-06-28T06:23:37.615Z