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Riesz transform and Riesz potentials for Dunkl transform. (English) Zbl 1145.44001

The authors study the analogues of the Riesz potential and the Riesz transforms for the Dunkl transform in this paper. They also study the boundedness of the Riesz potentials as well as the related Bessel potentials. The proof of \(L^p\) boundedness for the weighted Riesz transform is given only in a very special case.

MSC:

43A32 Other transforms and operators of Fourier type
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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References:

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