Boundedness of high order Riesz-Bessel transformations generated by generalized shift operator on B\(a\) spaces
type: Item
instance of: scholarly article
title: Boundedness of high order Riesz-Bessel transformations generated by generalized shift operator on B\(a\) spaces
zbMATH Open document ID: 1059.47053
DOI: 10.1142/S0252959903000074
published in: Chinese Annals of Mathematics. Series B
publication date: 2004-02-05T00:00:00Z
review text: It is shown that the Riesz--Bessel transformations \(R_{B_j}\), \(j=1,2,\dots, n-1, \) are bounded on the space \(B_a\), where \[ B_a= \{ f: f \in \cap_{m=1}^{\infty} B_m, R_f>0 \}, \] \[ \| f\| _{B_a}=\inf_{\alpha>0}\{ 1/\alpha: I(f,\alpha)\leq 1\}, \] \[ B_m= L_{p_m,\nu} (\mathbb{R}_n^+)=\left\{ f: \| f\| _{ L_{p_m, \nu}}\equiv \bigg(\int_{\mathbb{R}^+_n} | f(x)| ^{p_m} x_n^{2 \nu} dx \bigg)^{1/p_m} < \infty \right\} \] and \(R_f\) is the radius of the convergence of the series \[ I(f,\alpha)=\sum_{m=1}^{\infty}a_m \| f\| _{B_m}^m \alpha^m, \] if and only if there exist constants \(\alpha\) and \(\beta\) such that the sequence \(\{p_m\}\) satisfies \(1<\alpha<p_m<\beta\) for all \(a_m\neq 0\).
reviewed by: Alexander Meskhi
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 1931575
zbMATH Keywords: Riesz--Bessel transformations
zbMATH Keywords: generalized shift operator
zbMATH Keywords: boundedness of operators
author: A. Serbetci
author: I. Ekincioglu
MaRDI profile type: Publication
full work available at URL: s0252959903000074
OpenAlex ID: W2233851944
description: scientific article; zbMATH DE number 1931575