English

Riesz potential and maximal function for Dunkl transform

Classical Analysis and ODEs 2017-09-01 v1

Abstract

We study weighted (Lp,Lq)(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,Lq)(L^1, L^q) estimate. We find a sharp constant in the weighted LpL^p-inequality, generalizing the results of W. Beckner and S. Samko.

Keywords

Cite

@article{arxiv.1708.09733,
  title  = {Riesz potential and maximal function for Dunkl transform},
  author = {D. V. Gorbachev and V. I. Ivanov and S. Yu. Tikhonov},
  journal= {arXiv preprint arXiv:1708.09733},
  year   = {2017}
}

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25 pages