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

2025/05/25 by Yanping Chen, Chen, Yanping, Xueting Han +1
Mathematics · #42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Primary: 42B35. Secondary: 42B25 #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.18974

openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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