Boundedness of singular integral operators of Calderón type
type: Item
instance of: scholarly article
title: Boundedness of singular integral operators of Calderón type
zbMATH Open document ID: 0542.42008
author: Takafumi Murai
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: A. Calderón, R. Coifman, A. McIntosh, Y. Meyer, G. David, and others have studied singular integral operators with kernels of type \[ C[h,\Phi]\quad(x,y)=(1/x-y)\quad(h\{\Phi(x)-\Phi(y)/(x-y)\} \] for complex-valued function h and real-valued functions \(\Phi\) [\textit{A. Calderón}, Proc. Natl. Acad. Sci. USA 53, 1092-1099 (1965; Zbl 0151.169), \textit{R. R. Coifman}, \textit{A. McIntosh, and \textit{Y. Meyer}}, Ann. Math., II. Ser. 116, 361-387 (1982; Zbl 0497.42012)]. They found out that C(h,\(\Phi]\) is of type 2 if h is infinitely differentiable and \(\Phi\) ' is essentially bounded. The purpose of this paper is to give a new proof of this theorem. The author will deduce this theorem from Calderón's theorem [loc.cit.] and so called ''good \(\lambda\) inequalities''.
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 3861752
zbMATH Keywords: singular integral operators of Calderón type
reviewed by: W. Kugler
MaRDI profile type: Publication
full work available at URL: pjaa.59.364
OpenAlex ID: W1994514448
cites work: COMMUTATORS OF SINGULAR INTEGRAL OPERATORS
cites work: Cauchy integrals on Lipschitz curves and related operators
cites work: On Commutators of Singular Integrals and Bilinear Singular Integrals
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: Q4751156
cites work: Q5607484
DOI: 10.3792/PJAA.59.364
description: scientific article; zbMATH DE number 3861752