D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov
Published 2017-08-31Version 1
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.
Paley-Wiener theorems for the Dunkl transform
Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $L^{2}$
Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line
![QR code for arXiv:1708.09733 [math.CA]](http://oss.arxitics.com/images/favicon.svg)