Some results on Dunkl analysis : A survey
Sif, M., Amri, B., Anker, J., Hassani, S., Mustapha, S. (2011). Some results on Dunkl analysis : A survey. EKB Journal Management System, 19(1), 78-81. doi: 10.1016/j.joems.2011.09.001
M. Sif; B. Amri; J-Ph Anker; S. Hassani; S. Mustapha. "Some results on Dunkl analysis : A survey". EKB Journal Management System, 19, 1, 2011, 78-81. doi: 10.1016/j.joems.2011.09.001
Sif, M., Amri, B., Anker, J., Hassani, S., Mustapha, S. (2011). 'Some results on Dunkl analysis : A survey', EKB Journal Management System, 19(1), pp. 78-81. doi: 10.1016/j.joems.2011.09.001
Sif, M., Amri, B., Anker, J., Hassani, S., Mustapha, S. Some results on Dunkl analysis : A survey. EKB Journal Management System, 2011; 19(1): 78-81. doi: 10.1016/j.joems.2011.09.001

Some results on Dunkl analysis : A survey

Journal of the Egyptian Mathematical Society
Volume 19, Issue 1, June 2011, Page 78-81  XML PDF (354.83 K)
DOI: 10.1016/j.joems.2011.09.001
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Authors
M. Sif email ; B. Amri; J-Ph Anker; S. Hassani; S. Mustapha
Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia
Abstract
In this article, we present a survey of some new results obtained in [2,8]. First, we give a geometric Paley–Wiener theorem for the Dunkl transform in the crystallographic case. Next we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension. We also investigate the Lp fi Lq boundedness properties of the Riesz potentials Ija and the related fractional maximal function Mj,a associated to the Dunkl transform. Finally we prove the Lp-boundedness, (1 < p< 1) of the Riesz transforms in the Dunkl setting.
Keywords
Dunkl operator; Paley–Wiener theorem; Generalized translations; Riesz potentials; Riesz transforms
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