Lebesgue boundedness of Riesz potential for (𝑘, 1)-generalized Fourier transform with radial piecewise power weights
https://doi.org/10.22405/2226-8383-2022-23-4-92-104
Abstract
In spaces with weight |𝑥|−1𝑣𝑘(𝑥), where 𝑣𝑘(𝑥) is the Dunkl weight, there is the (𝑘, 1)- generalized Fourier transform. Harmonic analysis in these spaces is important, in particular, in problems of quantum mechanics. Recently, for the (𝑘, 1)-generalized Fourier transform, the
Riesz potential was defined and the (𝐿𝑝,𝐿𝑞)-inequality with radial power weights was proved for it, which is an analogue of the well-known Stein–Weiss inequality for the classical Riesz potential and the Dunkl–Riesz potential. In the paper, this result is generalized to the case of radial piecewise power weights. Previously, a similar inequality was proved for the Dunkl–Riesz potential.
Supporting agencies: The research was supported by a grant from the Russian Science Foundation № 18-11-00199, https://rscf.ru/ project/18-11-00199/.
About the Author
Valerii Ivanovich Ivanov
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
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For citations:
Ivanov V.I. Lebesgue boundedness of Riesz potential for (𝑘, 1)-generalized Fourier transform with radial piecewise power weights. Chebyshevskii Sbornik. 2022;23(4):92-104. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-92-104
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