Hölder estimates for the Cauchy integral on a Lipschitz contour
type: Item
instance of: scholarly article
title: Hölder estimates for the Cauchy integral on a Lipschitz contour
zbMATH Open document ID: 0674.45013
DOI: 10.1216/JIE-1988-1-3-435
author: William Mclean
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Gamma\) be a Lipschitz contour. Note that a Lipschitz contour may have (infinitely many) corners, but may not posses cusps. The author considers the singular integral operator \[ (Su)(x)=u(x)+1/\pi i\int_{\Gamma}u(y)-u(x)/(y-x)dy,\quad x\in \Gamma, \] where \(u\in H^{\alpha}(\Gamma)\), \(0<\alpha <1\), and estimates the norm of the operator \(S\in B(H^{\alpha}(\Gamma))\). Moreover, a theorem analogous to the Plemelj-Sokhotskij theorem for the integral 1/2\(\pi\) \(i\int_{\Gamma}u(y)dy/(y-z)\) is obtained.
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 47Gxx
zbMATH DE Number: 4103713
zbMATH Keywords: Hölder estimates
zbMATH Keywords: Cauchy integral
zbMATH Keywords: Lipschitz contour
zbMATH Keywords: singular integral operator
zbMATH Keywords: Plemelj-Sokhotskij theorem
reviewed by: Zbigniew Binderman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4103713