On the monotonicity of some singular integral operators
type: Item
instance of: scholarly article
title: On the monotonicity of some singular integral operators
zbMATH Open document ID: 1256.45004
author: Lothar von Wolfersdorf
author: Peter Junghanns
published in: Mathematical Methods in the Applied Sciences
publication date: 2012-06-29T00:00:00Z
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6051067
zbMATH Keywords: singular integral operators
zbMATH Keywords: monotonicity
zbMATH Keywords: weakly singular kernels
zbMATH Keywords: logarithmic kernels
zbMATH Keywords: Cauchy singular integral operator
zbMATH Keywords: maximal monotone
MaRDI profile type: Publication
full work available at URL: mma.1605
OpenAlex ID: W1979391395
cites work: Q5715735
cites work: Monotonicity Methods for Nonlinear Singular Integral and Integro‐Differential Equations
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cites work: Cordial Volterra Integral Equations 1
cites work: Q4777920
cites work: Carleson curves, Muckenhoupt weights, and Toeplitz operators
cites work: Q5820721
cites work: Q3857336
cites work: On the theory of convolution equations of the third kind
cites work: On the theory of convolution equations of the third kind. II
DOI: 10.1002/MMA.1605
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review text: The authors study monotone singular integral operators, maximal monotone operators, adjoint operators and equations with logarithmic kernels.NEWLINENEWLINE The singular integral operators are of the form \(Q= qS\), where \(S\) is the Cauchy singular integral operator on the interval \((0,1)\) and \(q\) is a power or logarithmic function.NEWLINENEWLINE The singular integral operators are proved to be monotone and maximal monotone in the spaces \(L^2\) with power weights.NEWLINENEWLINE The equations with logarithmic kernels are two integral equations with weakly singular kernels of logarithmic type.
reviewed by: Dan-Mircea Borş
description: scientific article; zbMATH DE number 6051067