Geodesic
Lebesgue boundedness of Riesz potential for $(k,1)$-generalized Fourier transform with radial piecewise power weights
Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 92-104

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In spaces with weight $|x|^{-1}v_k(x)$, where $v_k(x)$ 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 $(L^p,L^q)$-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.
Keywords: $(k,1)$-generalized Fourier transform, Riesz potential. 
@article{CHEB_2022_23_4_a7,
     author = {V. I. Ivanov},
     title = {Lebesgue boundedness of {Riesz} potential for $(k,1)$-generalized {Fourier} transform with radial piecewise power weights},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {92--104},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a7/}
}
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V. I. Ivanov. Lebesgue boundedness of Riesz potential for $(k,1)$-generalized Fourier transform with radial piecewise power weights. Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 92-104. http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a7/