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 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 fun... Mehr ...
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| Dokumenttyp: | Artikel |
| Erscheinungsdatum: | 2024 |
| Verlag/Hrsg.: |
Ele-Math
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| Schlagwörter: | Generalized Orlicz spaces / Amemiya quasi-norm / Luxemburg quasi-norm / Orlicz quasi-norm / Quasi-Banach function space / Weak Fatou property |
| Sprache: | Englisch |
| Permalink: | https://search.fid-benelux.de/Record/base-27526460 |
| Datenquelle: | BASE; Originalkatalog |
| Powered By: | BASE |
| Link(s) : | https://idus.us.es/handle//11441/156675 |
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.