Fourier multipliers for \(L_ p (\mathbb{R}^ n)\) via \(q\)-variation
type: Item
instance of: scholarly article
title: Fourier multipliers for \(L_ p (\mathbb{R}^ n)\) via \(q\)-variation
zbMATH Open document ID: 0865.42010
author: Quanhua Xu
published in: Pacific Journal of Mathematics
publication date: 1996-12-17T00:00:00Z
review text: We give a new sufficient condition for a function \(m\) to be a Fourier multiplier of \(L_p (\mathbb{R}^n)\) via its \(q\)-variation on dyadic rectangles, that is, if \(m\) is of bounded \(q\)-variation uniformly on dyadic rectangles, then \(m\) is a Fourier multiplier for \(L_p (\mathbb{R}^n)\) whenever \(1< p< \infty\) and \(|1/p- 1/2|<1/q\). This solves a problem posed by Coifman, Rubio de Francia and Semmes, who had considered only the one-dimensional case.
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 950237
zbMATH Keywords: Littlewood-Paley theory
zbMATH Keywords: Fourier multiplier
zbMATH Keywords: \(q\)-variation
zbMATH Keywords: dyadic rectangles
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.287
OpenAlex ID: W2591845281
DOI: 10.2140/PJM.1996.176.287
description: scientific article; zbMATH DE number 950237