Convolution operator and maximal function for the Dunkl transform
نویسندگان
چکیده
منابع مشابه
Convolution and Maximal Function For
For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a m...
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On the real line, the Dunkl operators are differential-difference operators introduced in 1989 by Dunkl [1] and are denoted by Λα, where α is a real parameter > −1/2. These operators are associated with the reflection group Z2 on R. The Dunkl kernel Eα is used to define the Dunkl transform α which was introduced by Dunkl in [2]. Rösler in [3] shows that the Dunkl kernels verify a product formul...
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Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2005
ISSN: 0021-7670,1565-8538
DOI: 10.1007/bf02807401