Characterization of fractional maximal operator and its commutators on Orlicz spaces in the Dunkl setting

On the Rd the Dunkl operators {Dk,j}j=1d are the differential-difference operators associated with the reflection group Z2d on Rd. In this paper, in the setting Rd we find necessary and sufficient conditions for the boundedness of the fractional maximal operator Mα,k on Orlicz spaces LΦ,k(Rd). As an application of this result we show that b∈ BMOk(Rd) if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ,k(Rd). © 2020, Springer Nature Switzerland AG.