Riesz potential and maximal function for Dunkl transform

2017/08/31 by Д. В. Горбачев, Gorbachev, D. V., В. И. Иванов +3
Mathematics · #33C45 #33C52 #42B10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1708.09733

openalex publication_date 2017/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study weighted (L^p, L^q)-boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy-Littlewood-Sobolev type inequality and weighted week (L¹, L^q) estimate. We find a sharp constant in the weighted L^p-inequality, generalizing the results of W. Beckner and S. Samko.

Citations

• Convolution operator and maximal function for the Dunkl transform

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