Boundedness and compactness of Heckman-Opdam two-wavelet multipliers
type: Item
instance of: scholarly article
title: Boundedness and compactness of Heckman-Opdam two-wavelet multipliers
zbMATH Open document ID: 1382.42008
author: Hatem Mejjaoli
published in: Journal of Pseudo-Differential Operators and Applications
publication date: 2017-12-13T00:00:00Z
review text: The behavior of hypergeometric Fourier transform has been investigated by several authors to solve the problems of wavelet theory, real Paley-Wiener theorems, uncertanity principles and so on. Using the properties of hypergeometric Fourier transform the two wavelet multipliers associated to Heckman-Opdam theory have been exposed and studied in this paper. The wavelet multipliers were introduced by \textit{Z. He} and \textit{M. W. Wong} [J. Aust. Math. Soc., Ser. B 40, No. 4, 437--446 (1999; Zbl 0937.35196)] and detailed in the book [Wavelet transforms and localization operators. Basel: Birkhäuser (2002; Zbl 1016.42017)] by \textit{M.-W. Wong}. The results studied in this paper generalized the various results of \textit{M. W. Wong} and \textit{Z. Zhang} [Integral Equations Oper. Theory 42, No. 4, 498--503 (2002; Zbl 1021.42018); Bull. Lond. Math. Soc. 34, No. 6, 739--744 (2002; Zbl 1048.47037)]. Moreover, the Schatten-von Neumann properties of above mentioned wavelet multipliers have been established. Also, the \(L^{p}\)-boundedness and compactness with the traces and trace class norm inequalities have been obtained.
reviewed by: Devendra Kumar
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 44A05
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 33C67
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 6818234
zbMATH Keywords: hypergeometric Fourier transform
zbMATH Keywords: Heckman-Opdam multipliers
zbMATH Keywords: Heckman-Opdam two-wavelet multipliers
zbMATH Keywords: Schatten-von Neumann class
MaRDI profile type: Publication
full work available at URL: s11868-017-0221-0
OpenAlex ID: W2751296425
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DOI: 10.1007/S11868-017-0221-0
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description: scientific article; zbMATH DE number 6818234