Cauchy integral and singular integral operator over closed Jordan curves

Ricardo Abreu Blaya; Juan Bory Reyes; Boris Kats

doi:10.1007/s00605-014-0656-9

Cauchy integral and singular integral operator over closed Jordan curves

Ricardo Abreu Blaya, Juan Bory Reyes, Boris Kats

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

This paper is mostly a review paper. It contains a description of old and recent results concerning the regularity conditions on a Jordan curve in the plane that imply the boundedness of the singular integral operator as well as the boundary behavior of the Cauchy type integral. These results are of significance for boundary value problems in domains with non-smooth and non-rectifiable boundaries.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Monatshefte fur Mathematik
Volume	176
Issue number	1
DOIs	https://doi.org/10.1007/s00605-014-0656-9
State	Published - Jan 2015
Externally published	Yes

Keywords

Boundary value problem
Cauchy integral
Singular integral operator

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10.1007/s00605-014-0656-9

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abstract = "This paper is mostly a review paper. It contains a description of old and recent results concerning the regularity conditions on a Jordan curve in the plane that imply the boundedness of the singular integral operator as well as the boundary behavior of the Cauchy type integral. These results are of significance for boundary value problems in domains with non-smooth and non-rectifiable boundaries.",

keywords = "Boundary value problem, Cauchy integral, Singular integral operator",

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KW - Singular integral operator

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Cauchy integral and singular integral operator over closed Jordan curves

Abstract

Keywords

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