Boundedness of singular integral operators of Calderón type. V
type: Item
instance of: scholarly article
title: Boundedness of singular integral operators of Calderón type. V
zbMATH Open document ID: 0608.42010
DOI: 10.1016/0001-8708(86)90038-1
author: Takafumi Murai
published in: Advances in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let BMO denote the totality of real functions f such that \(\| f\|_{BMO}=\sup (1/| I|)\int_{I}| f(x)-m_ If| dx<\infty,\) where \(m_ If=(1/| I|)\int_{I}f(x)dx\) and the supremum is taken over all finite intervals I. For a real locally integrable function \(\phi\) define a kernel \(C[\phi](x,y)=1/\{(x-y)+i(\Phi (x)-\Phi (y))\},\) where \(\Phi (x)=\int^{x}_{0}\phi (s)ds.\) C[\(\phi\) ] denotes the corresponding singular integral operator from \(L^ 2\) to \(L^ 2\). Using severals lemmas, the author proves the following theorem. For any \(\phi \in BMO_ r\), \(\| C[\phi]\| \leq Const(1+\| \phi \|^ 2_{BMO}).\) [For part IV see Hiroshima Math. J. 14(1985), 511-525 (1984; Zbl 0562.42008).]
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 3983820
zbMATH Keywords: singular integral operator
reviewed by: Wolfram Luther
MaRDI profile type: Publication
full work available at URL: 0001-8708(86)90038-1
OpenAlex ID: W2024265555
cites work: Cauchy integrals on Lipschitz curves and related operators
cites work: La solution des conjectures de Calderon
cites work: L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
cites work: Opérateurs intégraux singuliers sur certaines courbes du plan complexe
cites work: Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon
cites work: Boundedness of singular integral operators of Calderón type. IV
description: scientific article; zbMATH DE number 3983820