Disjointly strictly singular inclusions between variable Lebesgue spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913835696259072 |
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| author | Hernández, Francisco L. Ruiz, César Sanchiz, Mauro |
| author_facet | Hernández, Francisco L. Ruiz, César Sanchiz, Mauro |
| contents | Disjointly strictly singular inclusions between variable Lebesgue spaces $L^{p(\cdot)}(μ)$ 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 $L^{p(\cdot)}(μ) \hookrightarrow L^{q(\cdot)}(μ)$ is not disjointly strictly singular. No restrictions on the exponent are imposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Disjointly strictly singular inclusions between variable Lebesgue spaces Hernández, Francisco L. Ruiz, César Sanchiz, Mauro Functional Analysis 46E30, 47B60 Disjointly strictly singular inclusions between variable Lebesgue spaces $L^{p(\cdot)}(μ)$ 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 $L^{p(\cdot)}(μ) \hookrightarrow L^{q(\cdot)}(μ)$ is not disjointly strictly singular. No restrictions on the exponent are imposed. |
| title | Disjointly strictly singular inclusions between variable Lebesgue spaces |
| topic | Functional Analysis 46E30, 47B60 |
| url | https://arxiv.org/abs/2406.14175 |