Riesz potential for $(k,1)$-generalized Fourier transform
Čebyševskij sbornik, Tome 22 (2021) no. 4, pp. 114-135
Voir la notice de l'article provenant de la source Math-Net.Ru
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. We define the Riesz potential for the $(k,1)$-generalized Fourier transform and prove for it, a $(L^q,L^p)$-inequality with radial power weights, which is an analogue of the well-known Stein–Weiss inequality for the classical Riesz potential. For the Riesz potential we calculate the sharp value of the $L^p$-norm with radial power weights. The sharp value of the $L^p$-norm with radial power weights for the classical Riesz potential was obtained independently by W. Beckner and S. Samko.
Keywords:
$(k,1)$-generalized Fourier transform, Riesz potential.
@article{CHEB_2021_22_4_a4,
author = {V. I. Ivanov},
title = {Riesz potential for $(k,1)$-generalized {Fourier} transform},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {114--135},
publisher = {mathdoc},
volume = {22},
number = {4},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_4_a4/}
}
V. I. Ivanov. Riesz potential for $(k,1)$-generalized Fourier transform. Čebyševskij sbornik, Tome 22 (2021) no. 4, pp. 114-135. http://geodesic.mathdoc.fr/item/CHEB_2021_22_4_a4/