Orlicz spaces associated to a quasi‑Banach function space: applications to vector measures and interpolation
The Orlicz spaces XΦ associated to a quasi-Banach function space X are defined by replacing the role of the space L1 by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this construction to the spaces L1w(m), L1(m) and L1(∥m∥) of integrable functions (in the w...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/134579 |
| Acceso en línea: | https://hdl.handle.net/11441/134579 https://doi.org/10.1007/s13348-020-00295-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Orlicz spaces Quasi-Banach function spaces Vector measures Complex interpolation |
| Sumario: | The Orlicz spaces XΦ associated to a quasi-Banach function space X are defined by replacing the role of the space L1 by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this construction to the spaces L1w(m), L1(m) and L1(∥m∥) of integrable functions (in the weak, strong and Choquet sense, respectively) in order to obtain the known Orlicz spaces LΦw(m) and LΦ(m) and the new ones LΦ(∥m∥). Therefore, we are providing a framework where dealing with different kind of Orlicz spaces in a unified way. Some applications to complex interpolation are also given. |
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