Disjointly strictly singular inclusions between variable Lebesgue spaces
Functional Analysis
2025-05-15 v1
Abstract
Disjointly strictly singular inclusions between variable Lebesgue spaces on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of -weak compactness (also called almost compactness) and disjoint strict singularity for variable Lebesgue space inclusions. For infinite measure any inclusion is not disjointly strictly singular. No restrictions on the exponent are imposed.
Cite
@article{arxiv.2406.14175,
title = {Disjointly strictly singular inclusions between variable Lebesgue spaces},
author = {Francisco L. Hernández and César Ruiz and Mauro Sanchiz},
journal= {arXiv preprint arXiv:2406.14175},
year = {2025}
}