Sparse domination for singular integral operators and their commutators in Dunkl setting with applications

Abstract

In this paper, we establish sparse dominations for the Dunkl-Calderón-Zygmund operators and their commutators in the Dunkl setting. As applications, we first define the Dunkl-Muckenhoupt $A_p$ weight and obtain the weighted bounds for the Dunkl-Calderón-Zygmund operators, as well as the two-weight bounds for their commutators. Moreover, we also obtain the boundedness of the Dunkl-Calderón-Zygmund operators on the extrapolation space of a family of Banach function spaces.