On some geometric properties of generalized Orlicz-Lorentz function spaces

摘要

In this article we continue investigations concerning generalized OrliczLorentz function spaces Λφ initiated in the papers (Foralewski, 2011) [29,30] (cf. also (Foralewski, 2008) [27,28]). First, it is shown that modular ρφ is orthogonally subadditive. Next, monotonicity properties are considered. In order to get sufficient conditions for uniform monotonicity of the space Λφ a strong condition of Δ2 type and the notion of regularity of the generated MusielakOrlicz function φ are introduced. Finally, criteria for non-squareness of Λφ are presented.