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arXiv · 2406.14175

Disjointly strictly singular inclusions between variable Lebesgue spaces

Francisco L. Hernández·César Ruiz·Mauro Sanchiz
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Abstract

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

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Francisco L. Hernández, César Ruiz, Mauro Sanchiz. 2024-06-20. Disjointly strictly singular inclusions between variable Lebesgue spaces. https://doi.org/10.1016/j.jmaa.2025.129634

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