Maximal operator on variable exponent spaces
Functional Analysis
2025-02-17 v1
Abstract
We explore the boundedness of the Hardy-Littlewood maximal operator on variable exponent spaces. Our findings demonstrate that the Muckenhoupt condition, in conjunction with Nekvinda's decay condition, implies the boundedness of even for unbounded exponents. This extends the results of Lerner, Cruz-Uribe and Fiorenza for bounded exponents. We also introduce a novel argument that allows approximate unbounded exponents by bounded ones while preserving the Muckenhoupt and Nekvinda conditions.
Cite
@article{arxiv.2502.10313,
title = {Maximal operator on variable exponent spaces},
author = {Daviti Adamadze and Lars Diening and Tengiz Kopaliani},
journal= {arXiv preprint arXiv:2502.10313},
year = {2025}
}