English

Disjointly strictly singular inclusions between variable Lebesgue spaces

Functional Analysis 2025-05-15 v1

Abstract

Disjointly strictly singular inclusions between variable Lebesgue spaces Lp()(μ)L^{p(\cdot)}(\mu) on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of LL-weak compactness (also called almost compactness) and disjoint strict singularity for variable Lebesgue space inclusions. For infinite measure any inclusion Lp()(μ)Lq()(μ)L^{p(\cdot)}(\mu) \hookrightarrow L^{q(\cdot)}(\mu) is not disjointly strictly singular. No restrictions on the exponent are imposed.

Keywords

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}
}
R2 v1 2026-06-28T17:13:13.855Z