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

TL;DR

This paper develops sparse domination techniques for Dunkl-Calderón-Zygmund operators and their commutators, leading to new weighted bounds and boundedness results in the Dunkl setting, extending classical harmonic analysis tools.

Contribution

It introduces sparse domination for Dunkl operators and their commutators, providing weighted bounds and boundedness in Banach function spaces, a novel extension in Dunkl analysis.

Findings

Established sparse domination for Dunkl-Calderón-Zygmund operators.

Derived weighted bounds for these operators and their commutators.

Proved boundedness on extrapolation spaces of Banach function spaces.

Abstract

In this paper, we establish sparse dominations for the Dunkl-Calder\'on-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-Calder\'on-Zygmund operators, as well as the two-weight bounds for their commutators. Moreover, we also obtain the boundedness of the Dunkl-Calder\'on-Zygmund operators on the extrapolation space of a family of Banach function spaces.