Boundedness of Fractional Maximal Operator and its Commutators on Generalized Orlicz-Morrey Spaces

Abstract

We consider generalized Orlicz-Morrey spaces including their weak versions . We find the sufficient conditions on the pairs and which ensures the boundedness of the fractional maximal operator from to and from to . As applications of those results, the boundedness of the commutators of the fractional maximal operator with on the spaces is also obtained. In all the cases the conditions for the boundedness are given in terms of supremal-type inequalities on weights , which do not assume any assumption on monotonicity of on r.