On spaces of integrable functions associated to vector measures and limiting real interpolation
We investigate which spaces are obtained when considering the limiting class of real interpolation spaces (0, q; J) for ordered Banach couples of spaces of (scalar) integrable functions with respect to a vector measure m, defined on a σ-algebra, with values in a Banach space. If m is in particular a...
| Autores: | , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2024 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/164113 |
| Acesso em linha: | https://hdl.handle.net/11441/164113 https://doi.org/10.1016/j.jmaa.2024.128573 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Extreme interpolation spaces Vector measures Lorentz-Zygmund spaces Optimal domain p-th power factorable operators Bidual (p, q)-power-concave operators |
| Resumo: | We investigate which spaces are obtained when considering the limiting class of real interpolation spaces (0, q; J) for ordered Banach couples of spaces of (scalar) integrable functions with respect to a vector measure m, defined on a σ-algebra, with values in a Banach space. If m is in particular a finite positive scalar measure, previous known results are derived from ours. Furthermore, we study the interpolation of p-th power factorable operators by the extreme real interpolation method (1, q; K). We also deduce interpolation results for the (1, q; K)-method that apply to other related classes of operators to p-th power factorable operators, such as bidual (p, q)-power-concave operators and q-concave operators. |
|---|