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arXiv · 2505.18974

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

Yanping Chen·Xueting Han
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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.

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Yanping Chen, Xueting Han. 2025-05-25. Sparse domination for singular integral operators and their commutators in Dunkl setting with applications. https://arxiv.org/abs/2505.18974

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