An inclusion property of Orlicz-Morrey spaces

Abstract

The Orlicz-Morrey spaces Lϕ,Φ (where Φ is a Young function and ϕ is a parameter for the Morrey spaces) are generalizations of Orlicz spaces and Morrey spaces. Inclusion properties between Orlicz spaces LΦ and between Morrey spaces are well known. In this study we will investigate the inclusion relation between Orlicz-Morrey spaces Lϕ1, Φ1 and Lϕ2, Φ2 with respect to Young functions Φ1, Φ2 and parameters ϕ1, ϕ2. Also, we give sufficient and necessary conditions for the inclusion property of these spaces, which are obtained through norm estimates for the characteristic functions of balls in ℝn. In addition, we shall give a sufficient and necessary condition for generalized Hölder’s inequality.