Boundedness of the Maximal and Singular Operators on Generalized Orlicz-Morrey Spaces

Abstract

We consider generalized Orlicz-Morrey spaces MF Phi,phi(R-n) including their weak versions. In these generalized spaces we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel. In all the cases the conditions for the boundedness are given either in terms of Zygmund- type integral inequalities on phi(r) without assuming any monotonicity property of phi(r), or in terms of supremal operators, related to phi(r).