Generalized Mixed Morrey Spaces

ABSTRACT In this paper, we introduce the generalized mixed Morrey spaces. We show that a generalized mixed Morrey space is the dual of a generalized mixed Hardy space. For a large class of generalized fractional integral operators, we give a necessary and sufficient condition for such operators to be bounded from one generalized mixed Morrey space to another. Moreover, we also prove the boundedness of the Hardy–Littlewood maximal operator and the generalized fractional maximal operator on such spaces.