Norm estimate of the Cauchy transform on \(L^p(\Omega)\)
type: Item
instance of: scholarly article
title: Norm estimate of the Cauchy transform on \(L^p(\Omega)\)
zbMATH Open document ID: 1091.42013
author: Milutin R. Dostanić
published in: Integral Equations and Operator Theory
publication date: 2006-02-07T00:00:00Z
review text: Let \(\Omega \) be a bounded domain in the complex plane. The Cauchy integral operator is defined by \[ Cf(z)=-\frac{1}{\pi}\int_\Omega \frac{f(\xi)}{\xi -z } dx dy, \quad \xi=x+iy. \] Two-sided estimates of the norm of \(Cf\) are given in the case when \(\Omega \) is the unit disc or the bounded simply connected domain with piecewise \(C^1\) boundary. A consequence is a better constant in Poincaré inequalities.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 30E20
zbMATH DE Number: 5003810
zbMATH Keywords: Cauchy transform
zbMATH Keywords: Bessel functions
zbMATH Keywords: Poincaré inequalities
Wikidata QID: Q60060315
reviewed by: Boris Rubin
MaRDI profile type: Publication
full work available at URL: s00020-002-1290-9
OpenAlex ID: W2071264161
DOI: 10.1007/S00020-002-1290-9
description: scientific article; zbMATH DE number 5003810