On the composition operator with variable integrability
Functional Analysis
2025-02-04 v2
Abstract
In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of the variable exponent, we provide necessary and sufficient conditions for this class of operators to be bounded and compact, respectively. In addition, we show the usefulness of the variable change to study weak compactness properties in the framework of non-standard spaces.
Cite
@article{arxiv.2410.22509,
title = {On the composition operator with variable integrability},
author = {Javier Henríquez-Amador and Carlos F. Álvarez},
journal= {arXiv preprint arXiv:2410.22509},
year = {2025}
}