Abstract
For the \((k,1)\)-generalized Fourier transform on the real line \(\mathbb{R}\), the Riesz transform is defined. For this transform, \(L^p\)-inequalities with power and piecewise power weights are proved for \(1<p<\infty\).
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This work was supported by the Russian Science Foundation under grant no. 18-11-00199, https://rscf.ru/project/18-11-00199/.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 360–373 https://doi.org/10.4213/mzm13791.
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Ivanov, V.I. Riesz Transform for the One-Dimensional \((k,1)\)-Generalized Fourier Transform. Math Notes 113, 356–367 (2023). https://doi.org/10.1134/S0001434623030057
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DOI: https://doi.org/10.1134/S0001434623030057