Riesz Potential and Maximal Function for Dunkl transform
نویسندگان
چکیده
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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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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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: Potential Analysis
سال: 2020
ISSN: 0926-2601,1572-929X
DOI: 10.1007/s11118-020-09867-z