Un analogue d'un théorème de Hardy pour la transformation de Dunkl</span><span lang="en" class="article-alt-title">An analogue of Hardy's theorem for the Dunkl transform期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Un analogue d'un théorème de Hardy pour la transformation de DunklAn analogue of Hardy's theorem for the Dunkl transform

Authors:	Léonard Gallardo Khalifa Trimèche

Institution:	1. Faculté des sciences, Département de mathématiques, parc de Grandmont, 37200 Tours, France;2. Faculté des sciences de Tunis, Département de mathématiques, campus Universitaire, 1060 Tunis, Tunisie

Abstract:	In this Note we give a generalization of Hardy's theorem for the Dunkl transform $F_{D}$ on $R^{d}$ . More precisely, for all a>0, b>0 and p,q∈1,+∞], we determine the measurable functions f such that $e^{a\|\|x\|\|^{2}} f∈ L_{k}^{p} (R^{d})$ and $e^{b\|\|y\|\|^{2}} F_{D} (f)∈ L_{k}^{q} (R^{d})$ , where $L_{k}^{p} (R^{d})$ are the L^p spaces associated with the Dunkl transform. *To cite this article: L. Gallardo, K. Trimèche, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 849–854.*

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