Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting

Abstract

On the real line, the Dunkl operators∀ν ≥ − 1 2 are differential-difference operators associated with the reflection group Z 2 on R, and on the R d the Dunkl operators { D k,j } d j=1 are the differential-difference operators associated with the reflection group Z d 2 on R d . In this paper, in the setting R we show that b ∈ BMO(R,dm ν ) if and only if the maximal commutator M b,ν is bounded on Orlicz spaces L Φ (R,dm ν ). Also in the setting R d we show that b ∈ BMO(R d ,h 2 k (x)dx) if and only if the maximal commutator M b,k is bounded on Orlicz spaces L Φ (R d ,h 2 k (x)dx).