\(L^p\)-boundedness of wavelet multipliers
type: Item
instance of: scholarly article
title: \(L^p\)-boundedness of wavelet multipliers
zbMATH Open document ID: 1080.42028
published in: Hokkaido Mathematical Journal
publication date: 2005-03-07T00:00:00Z
review text: If \(\varphi\in L^2({\mathbb R}^n)\cap L^\infty({\mathbb R}^n)\) is such that \(\| \varphi \|_2=1\), and \(\sigma\in L^\infty({\mathbb R}^n)\), in this paper the corresponding wavelet multiplier is the linear operator \(P_{\sigma,\varphi}\) such that \[ (P_{\sigma,\varphi}u,v)_2 =(2\pi)^{-n} \int_{{\mathbb R}^n} \sigma(\xi)(u,\pi(\xi)\varphi)_2 (\pi(\xi)\varphi,v)_2\, d\xi\quad (u,v\in\mathcal S), \] where \((\pi(\xi)\varphi)(x)= e^{ix\cdot\xi}\varphi(x)\). The authors give conditions on the symbol \(\sigma\) to ensure that \(P_{\sigma,\varphi}\) is a bounded operator on \(L^2({\mathbb R}^n)\), and on \(L^p({\mathbb R}^n)\) for \(4/3<p<4\).
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 2140986
zbMATH Keywords: Fourier multipliers
zbMATH Keywords: wavelet multipliers
zbMATH Keywords: unitary representations
zbMATH Keywords: boundedness
author: Bolin Ma
author: M. W. Wong
reviewed by: Joan Cerdà
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1285851914
OpenAlex ID: W2002812256
DOI: 10.14492/HOKMJ/1285851914
description: scientific article; zbMATH DE number 2140986