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An LP version of Hardy's theorem for the Dunkl transform

Part of: Metric geometry Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Léonard Gallardo  and
Khalifa Trimèche
Léonard Gallardo
Affiliation:
Faculté des Sciences, Département de Mathématiques, Parc de Grandmont, 37200 Tours, France e-mail: gallardo@univ-tours.fr
Khalifa Trimèche
Affiliation:
Faculté des Sciences de Tunis, Départment de Mathématiques, Campus Universitaire, 1060 Tunis, Tunisie e-mail: khlifa.trimeche@fst.rnu.tn
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Abstract

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In this paper, we give a generalization of Hardy's theorems for the Dunkl transform ℱD on ℝd. More precisely for all a > 0, b > 0 and p, q ∈ [1, + ∞], we determine the measurable functions f on ℝd such that where are the Lebesgue spaces associated with the Dunkl transform.

Keywords

Dunkl transformHardy's theorem

MSC classification

Secondary: 51F15: Reflection groups, reflection geometries 43A32: Other transforms and operators of Fourier type
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 371 - 386
Copyright
Copyright © Australian Mathematical Society 2004

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