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 $M_{b,\alpha}$ from the Dunkl-type modified Morrey space $\widetilde{{\cal M}}_{p,\lambda,\alpha}(R)$ to $\widetilde{{\cal M}}_{p,\lambda,\alpha}(R)$ for all $1 < p < \infty$ when $b \in BMO_{\alpha}(R)$ are proved.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 3
Year: 2020

DOI: 10.12732/ijam.v33i3.9

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