Linear and bilinear multiplier operators for the Dunkl transform
type: Item
instance of: scholarly article
title: Linear and bilinear multiplier operators for the Dunkl transform
zbMATH Open document ID: 1209.42006
author: Béchir Amri
author: Abdessalem Gasmi
author: Mohamed Sifi
published in: Mediterranean Journal of Mathematics
publication date: 2011-01-25T00:00:00Z
review text: The paper treats the problem of \(L^p\) estimates for linear and bilinear multiplier operators for the Dunkl transform in the one dimensional case. Using Hörmander's technique and an explicit formula for the Dunkl translation operator, an analogue of the celebrated Hörmander multiplier theorem is proved in the Dunkl setting. In the bilinear case a strategy of Coifman and Meyer is applied to receive an \(L^p\) estimate for the bilinear multiplier operators.
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 46F12
zbMATH DE Number: 5841052
zbMATH Keywords: Dunkl transform
zbMATH Keywords: multiplier operator
zbMATH Keywords: Littlewood-Paley theory
reviewed by: Krzysztof Stempak
MaRDI profile type: Publication
full work available at URL: s00009-010-0057-9
OpenAlex ID: W2010989965
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DOI: 10.1007/S00009-010-0057-9
description: scientific article; zbMATH DE number 5841052