Convolution operators and Bochner-Riesz means on Herz-type Hardy spaces in the Dunkl setting
type: Item
instance of: scholarly article
title: Convolution operators and Bochner-Riesz means on Herz-type Hardy spaces in the Dunkl setting
zbMATH Open document ID: 1213.44003
DOI: 10.1155/2010/204509
author: Abdessalem Gasmi
author: Fethi Soltani
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/229068
review text: For \(T\in \mathcal{S}'(\mathbb{R})\) and \(f\in \mathcal{S}(\mathbb{R})\), the Dunkl convolution product \(T\ast_{\alpha}f\) is defined by \[ T\ast_{\alpha}f(x)=\langle T(y), \tau_x f(-y)\rangle,\quad x\in \mathbb{R}, \] where \(\tau_x\) is the Dunkl translation operator. The author investigates the Dunkl convolution operators on Herz-type Hardy spaces \(\mathcal{H}_{\alpha,2}^{p}\) and establishes a version of multiplier theorem for the maximal Bochner-Riesz operators on the Herz-type Hardy spaces \(\mathcal{H}_{\alpha,\infty}^{p}\). Some related results are contained in the paper by \textit{S. Lu} and \textit{D. Yang} [Proc. Am. Math. Soc. 126, No.~11, 3337--3346 (1998; Zbl 0905.42007)].
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 5847811
zbMATH Keywords: Dunkl convolution
zbMATH Keywords: Herz-type Hardy spaces
zbMATH Keywords: Bochner-Riesz means
zbMATH Keywords: multiplier
Wikidata QID: Q58651713
MaRDI profile type: Publication
OpenAlex ID: W2158471600
cites work: \(H^p\) spaces of several variables
cites work: Multiplier theorems for Herz type Hardy spaces
cites work: Differential-Difference Operators Associated to Reflection Groups
cites work: Integral Kernels with Reflection Group Invariance
cites work: The Dunkl transform
cites work: Q5440521
cites work: Q3138332
cites work: Dunkl transform on R and convolution product on new spaces of distributions
cites work: \(L^{p}\)-Fourier multipliers for the Dunkl operator on the real line.
cites work: Q5562752
description: scientific article; zbMATH DE number 5847811