This article is cited in 1 paper

Riesz Transform for the One-Dimensional $(k,1)$-Generalized Fourier Transform

V. I. Ivanov

Tula State University

Abstract: 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 $1<p<\infty$.

Keywords: weight function, generalized Fourier transform, Riesz transform.

UDC: 517.5

MSC: 42A38

Received: 31.10.2022

DOI: 10.4213/mzm13791

 English version: Mathematical Notes, 2023, 113:3, 356–367

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