2022-07-272022-07-272020Campo 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)0022-247Xhttps://hdl.handle.net/11441/135915We 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.application/pdf18engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Banach function spaceVector measuresOrlicz spacesOrlicz normLuxemburg normStrictly monotone norminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.jmaa.2020.124302