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In this paper, we investigate the boundedness of maximal operator and itscommutators in generalized Orlicz-Morrey spaces on the spaces of homogeneoustype. As an application of this boundedness, we give necessary and sufficientcondition for the Adams type boundedness of fractional integral and itscommutators in these spaces. We also discuss criteria for the boundedness ofthese operators in Orlicz spaces.

A characterization for fractional integral and its commutators in Orlicz and generalized Orlicz-Morrey spaces on spaces of homogeneous type