Weak-type \((1,1)\) bounds for oscillatory singular integrals with rational phases
type: Item
instance of: scholarly article
zbMATH Open document ID: 1258.42011
author: Magali Folch-Gabayet
author: James Wright
published in: Studia Mathematica
publication date: 2012-07-13T00:00:00Z
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 6055445
zbMATH Keywords: singular integral
zbMATH Keywords: rational phase
zbMATH Keywords: weak-type \((1,1)\)
zbMATH Keywords: Hardy space
MaRDI profile type: Publication
full work available at URL: sm210-1-4
OpenAlex ID: W2068920633
DOI: 10.4064/SM210-1-4
title: Weak-type \((1,1)\) bounds for oscillatory singular integrals with rational phases
review text: The authors consider singular integral operators \(T\) on \(\mathbb R\), defined by NEWLINE\[NEWLINETf(x)=\text{p.v.}\int_{-\infty}^\infty \mathrm e^{\mathrm iR(y)}y^{-1}f(x-y)\,dy,NEWLINE\]NEWLINE where \(R(x)=P(x)/Q(x)\) is a rational function with real coefficients. They give that \(T\) is weak-type \((1,1)\) with bounds depending only on the degrees of \(P\) and \(Q\). They comment also that it is not always the case that these operators map the Hardy space \(H^1(\mathbb R)\) to \(L^1(\mathbb R)\) and characterize those rational phases \(R(x)\) which map \(H^1(\mathbb R)\) to \(L^1(\mathbb R)\).
reviewed by: Kôzô Yabuta
description: scientific article; zbMATH DE number 6055445