Geodesic
Riesz Transform for the One-Dimensional $(k,1)$-Generalized Fourier Transform
Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 360-373

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For the $(k,1)$-generalized Fourier transform on the real line $\mathbb{R}$, the Riesz transform is determined. For this transform, $L^p$-inequalities with power and piecewise power weights are proved for $1$.
Keywords: weight function, generalized Fourier transform, Riesz transform. 
@article{MZM_2023_113_3_a3,
     author = {V. I. Ivanov},
     title = {Riesz {Transform} for the {One-Dimensional} $(k,1)${-Generalized} {Fourier} {Transform}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {360--373},
     publisher = {mathdoc},
     volume = {113},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a3/}
}
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V. I. Ivanov. Riesz Transform for the One-Dimensional $(k,1)$-Generalized Fourier Transform. Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 360-373. http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a3/