Journal of Lie Theory 19 (2009), No. 4, 725--734
Copyright Heldermann Verlag 2009
Riesz Potentials and Fractional Maximal Function for the Dunkl Transform
Sallam Hassani
University of Tunis El Manar, Faculty of Sciences, Dept. of Mathematics, 2092 Tunis, Tunisia
sallem.h@gmail.com
Sami Mustapha
Institut Mathématiques de Jussieu, 175 Rue de Chevaleret, 75013 Paris, France
sam@math.jussieu.fr
Mohamed Sifi
University of Tunis El Manar, Faculty of Sciences, Dept. of Mathematics, 2092 Tunis, Tunisia
mohamed.sifi@fst.rnu.tn
[Abstract-pdf]
We investigate the $L^p \rightarrow L^q$ boundedness properties of the Riesz potentials $I_{\alpha}^{\kappa}$ and the related fractional maximal function $M_{\kappa,\alpha}$ associated to the Dunkl transform.
Keywords: Riesz potentials, Fractional maximal function.
MSC: 33C52; 43A32, 33C80, 22E30
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