ON THE BOUNDEDNESS OF DUNKL-TYPE MAXIMAL COMMUTATORS IN THE DUNKL-TYPE MODIFIED MORREY SPACES

Abstract

In this paper we consider the generalized shift operator, associated with the Dunkl operator and we investigate maximal commutators, commutators of singular integral operators and commutators of the fractional integral operators associated with the generalized shift operator. The boundedness of the Dunkl-type maximal commutator Mb,α from the Dunkl-type modified Morrey space M̃p,λ,α(R) to M̃p,λ,α(R) for all 1 < p < ∞ when b ∈ BMOα(R) are proved. AMS Subject Classification: 42B20, 42B25, 42B35