Orlicz-Morrey spaces and the Hardy-Littlewood maximal function

We prove basic properties of Orlicz-Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy-Littlewood maximal operator M from one Orlicz-Morrey space to another. For example, if f is an element of L(log L) (R-n), then M f is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of M, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.