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arXiv · 1708.09733

Riesz potential and maximal function for Dunkl transform

D. V. Gorbachev·V. I. Ivanov·S. Yu. Tikhonov
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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 $(L^1, L^q)$ estimate. We find a sharp constant in the weighted $L^p$-inequality, generalizing the results of W. Beckner and S. Samko.

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D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov. 2017-08-31. Riesz potential and maximal function for Dunkl transform. https://arxiv.org/abs/1708.09733

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