Cauchy integral and singular integral operator over closed Jordan curves

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• 作者：Ricardo Abreu Blaya (1)
  Juan Bory Reyes (2)
  Boris Kats (3)
  
  1. Facultad de Inform谩tica y Matem谩tica ; Universidad de Holgu铆n ; 80100聽 ; Holgu铆n ; Cuba
  2. Departamento de Matem谩tica ; Universidad de Oriente ; 90500聽 ; Santiago de Cuba ; Cuba
  3. Lobachevskii Institute of Mathematics and Mechanics ; Kazan Federal University ; Kremlevskaya Street ; 18 ; Kazan ; Tatarstan ; 420008 ; Russia
  
• 关键词：Cauchy integral ; Singular integral operator ; Boundary value problem ; Primary 30E20 ; 30E25 ; Secondary 45E05
• 刊名：Monatshefte für Mathematik
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：176
• 期：1
• 页码：1-15
• 全文大小：192 KB
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• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081

文摘

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.