A transference theorem for the Dunkl transform and its applications
نویسندگان
چکیده
منابع مشابه
A Transference Theorem for the Dunkl Transform and Its Applications
For a family of weight functions invariant under a finite reflection group, we show how weighted Lp multiplier theorems for Dunkl transform on the Euclidean space Rd can be transferred from the corresponding results for hharmonic expansions on the unit sphere Sd of Rd+1. The result is then applied to establish a Hörmander type multiplier theorem for the Dunkl transform and to show the convergen...
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl Transform
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.
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl transform
Using a generalized spherical mean operator, we obtain the generalizationof Titchmarsh's theorem for the Dunkl transform for functions satisfyingthe Lipschitz condition in L2(Rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.
متن کاملGENERALIZATION OF TITCHMARSH'S THEOREM FOR THE DUNKL TRANSFORM IN THE SPACE $L^P(R)$
In this paper, using a generalized Dunkl translation operator, we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(psi,p)$-Lipschitz Dunkl condition in the space $mathrm{L}_{p,alpha}=mathrm{L}^{p}(mathbb{R},|x|^{2alpha+1}dx)$, where $alpha>-frac{1}{2}$.
متن کاملgeneralization of titchmarsh's theorem for the dunkl transform
using a generalized spherical mean operator, we obtain the generalizationof titchmarsh's theorem for the dunkl transform for functions satisfyingthe lipschitz condition in l2(rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2010
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2010.03.006