When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?
We study the equivalence between the Orlicz and Luxemburg (quasi-) norms in the context of the generalized Orlicz spaces associated to an N-function Φ and a (quasi-) Banach function space X over a positive finite measure μ. We show that the Orlicz and the Luxemburg spaces do not coincide in general,...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/135915 |
| Acceso en línea: | https://hdl.handle.net/11441/135915 https://doi.org/10.1016/j.jmaa.2020.124302 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach function space Vector measures Orlicz spaces Orlicz norm Luxemburg norm Strictly monotone norm |
| Sumario: | We study the equivalence between the Orlicz and Luxemburg (quasi-) norms in the context of the generalized Orlicz spaces associated to an N-function Φ and a (quasi-) Banach function space X over a positive finite measure μ. We show that the Orlicz and the Luxemburg spaces do not coincide in general, and also that under mild requirements (σ-Fatou property, strictly monotone renorming) the coincidence holds. We use as a technical tool the classes LΦ w(m), LΦ(m) and LΦ( m ) of Orlicz spaces of scalar integrable functions with respect to a Banach space-valued countably additive vector measure m, providing also some new results on these spaces. |
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