Equivalent quasi-norms on generalized Orlicz spaces
In this paper we show that the equivalence among the classical quasi-norms of the generalized Orlicz spaces XΦ — the Orlicz quasi-norm, the Luxemburg quasi-norm and the Amemiya quasi-norm — holds under some mild conditions on the underlying quasi-Banach function space X — mainly the weak Fatou prope...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/156675 |
| Acesso em linha: | https://hdl.handle.net/11441/156675 https://doi.org/10.7153/mia-2023-26-26 |
| Access Level: | acceso abierto |
| Palavra-chave: | Generalized Orlicz spaces Amemiya quasi-norm Luxemburg quasi-norm Orlicz quasi-norm Quasi-Banach function space Weak Fatou property |
| Resumo: | In this paper we show that the equivalence among the classical quasi-norms of the generalized Orlicz spaces XΦ — the Orlicz quasi-norm, the Luxemburg quasi-norm and the Amemiya quasi-norm — holds under some mild conditions on the underlying quasi-Banach function space X — mainly the weak Fatou property — improving previous results of [R. DEL CAMPO, A. FERNANDEZ ´ , F. MAYORAL, F. NARANJO AND E. A. SANCHEZ ´ -PEREZ ´ , When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?, J. Math. Anal. Appl. 249, 1 (2020)] for which some lattice convexity requirements for the quasi-Banach function space X were needed. |
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