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Cauchy integral and singular integral operator over closed Jordan curves

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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.

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Acknowledgments

The authors are very thankful to the anonymous referee for his/her valuable remarks and suggestions that have considerably improved this article.

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Correspondence to Boris Kats.

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Communicated by A. Constantin.

B. Kats is partially supported by Russian Foundation for Basic Researches, grants 12-01-00636-a, 13-01-00322-a and 12-01-97015-r-povolzhie-a.

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Blaya, R.A., Reyes, J.B. & Kats, B. Cauchy integral and singular integral operator over closed Jordan curves. Monatsh Math 176, 1–15 (2015). https://doi.org/10.1007/s00605-014-0656-9

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