Characterization of the boundedness of fractional maximal operator and its commutators in Orlicz and generalized Orlicz–Morrey spaces on spaces of homogeneous type

In this paper, we establish the necessary and sufficient conditions for the boundedness of fractional maximal operator Mα and the fractional maximal commutators Mb,α in Orlicz LΦ(X) and generalized Orlicz–Morrey spaces MΦ,φ(X) on spaces of homogeneous type X= (X, d, μ) in the sense of Coifman-Weiss. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.