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Journal of Mathematics
Volume 2014 (2014), Article ID 702151, 7 pages
http://dx.doi.org/10.1155/2014/702151
Research Article

Weighted -Inequalities for the Dunkl Transform

1Department of Mathematics, Preparatory Institute of Engineer Studies of Tunis, University of Tunis, Montfleury, 1089 Tunis, Tunisia
2Laboratory LR11ES11, Faculty of Sciences of Tunis, University of Tunis El Manar, 1060 Tunis, Tunisia

Received 2 May 2014; Revised 15 October 2014; Accepted 15 October 2014; Published 6 November 2014

Academic Editor: Roberto A. Kraenkel

Copyright © 2014 Chokri Abdelkefi and Faten Rached. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give, for , weighted -inequalities for the Dunkl transform, using, respectively, the modulus of continuity of radial functions and the Dunkl convolution in the general case. As application, we obtain, in particular, the integrability of this transform on Besov-Lipschitz spaces.