Article
When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?
Author/s | Campo Acosta, Ricardo del
Fernández Carrión, Antonio Mayoral Masa, Fernando Naranjo Naranjo, Francisco José Sánchez Pérez, Enrique A. |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2020 |
Deposit Date | 2022-07-27 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Junta de Andalucía Ministerio de Ciencia, Innovación y Universidades (MICINN). España |
Project ID. | FQM-133
MTM2016-77054-C2-1-P2 |
Citation | Campo Acosta, R.d., Fernández Carrión, A., Mayoral Masa, F., Naranjo Naranjo, F.J. y Sánchez Pérez, E.A. (2020). When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?. Journal of Mathematical Analysis and Applications, 491 (1, art. nº124302) |
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