Maximal Subspaces of L1-Spaces of a Vector Measure with Lower p-Estimate
[EN] We introduce and characterize a new class of subspaces V-p(m) of L-1(m) associated with a vector measure m, consisting of functions whose associated measure has finite p-variation. We establish that these subspaces are maximal with respect to operators acting on Banach function spaces with a lo...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/226733 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/226733 |
| Access Level: | acceso abierto |
| Palabra clave: | Lattice concavity Lower p-estimate Vector measure Integration map P-finite variation (p,1)-Summing operator |
| Sumario: | [EN] We introduce and characterize a new class of subspaces V-p(m) of L-1(m) associated with a vector measure m, consisting of functions whose associated measure has finite p-variation. We establish that these subspaces are maximal with respect to operators acting on Banach function spaces with a lower p-estimate, meaning they are the largest subspaces of integrable functions that retain this property. Furthermore, we demonstrate that these spaces facilitate the study of restrictions of operators to subspaces where the lower p-estimate is preserved. We prove that if a vector measure induces a (p, 1)-summing integration operator, then it has finite p-variation, and the space L-1(m) coincides with the subspace of integrable functions satisfying a lower p-estimate V-p(m). As an application, we show that the optimal domain of positive operators on (p, 1)-concave Banach lattices, operators on Banach spaces of cotype p, and operators on 2-concave Banach lattices necessarily possess a lower p-estimate or lower 2-estimate, respectively. |
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