منابع مشابه
Riesz Transform and Riesz Potentials for Dunkl Transform
Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.
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Stein’s higher Riesz transforms are translation invariant operators on L2(Rn) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete series representations for hyperboloids associated to the indefini...
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 کاملPrincipal Values for Riesz Transforms and Rectifiability
Let E ⊂ R with H(E) < ∞, where H stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit
متن کاملAn Uncertainty Principle for the Dunkl Transform
The Dunkl transform is an integral transform on R" which generalises the classical Fourier transform. On suitable function spaces, it establishes a natural correspondence between the action of multiplication operators on one hand and so-called Dunkl operators on the other. These are differential-difference operators, generalising the usual partial derivatives, which are associated with a finite...
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ژورنال
عنوان ژورنال: Annales mathématiques Blaise Pascal
سال: 2012
ISSN: 1259-1734,2118-7436
DOI: 10.5802/ambp.312