Maximal operator in H\"older spaces
Functional Analysis
2023-03-30 v1
Abstract
We study the maximal operator on the variable exponent H\"older spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property. Let us stress that there are no assumptions on the regularity of the variable exponent and the variable exponent can touch values and . Furthermore, the continuity of the maximal operator between H\"older spaces is investigated. Those results are new even in the Euclidean setting.
Cite
@article{arxiv.2303.16713,
title = {Maximal operator in H\"older spaces},
author = {Piotr Michał Bies and Michał Gaczkowski and Przemysław Górka},
journal= {arXiv preprint arXiv:2303.16713},
year = {2023}
}