Cauchy integral and singular integral operator over closed Jordan curves

被引：0
作者：
Ricardo Abreu Blaya
Juan Bory Reyes
Boris Kats
机构：
[1] Universidad de Holguín,Facultad de Informática y Matemática
[2] Universidad de Oriente,Departamento de Matemática
[3] Kazan Federal University,Lobachevskii Institute of Mathematics and Mechanics
来源：
Monatshefte für Mathematik | 2015年 / 176卷
关键词：
Cauchy integral; Singular integral operator; Boundary value problem; Primary 30E20; 30E25; Secondary 45E05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：1 / 15
页数：14
相关论文
共 53 条
  • [1] Bari NK(1956)Best approximations and differential properties of two conjugate functions Trudy Moskov. Mat. Obšč (Russian) 5 483-522
  • [2] Stečkin SB(1973)A one-dimensional singular operator with continuous density along a closed curve Dokl. Akad. Nauk SSSR (Russian) 209 1257-1260
  • [3] Babaev AA(2003)One-dimensional singular integral equations Complex Var. Theory Appl. 48 483-493
  • [4] Salaev VV(1988)Approximation by Lipschitz functions and its application to boundary value of Cauchy-type integrals (English). Approximation and optimization, Proc. Int. Semin., Havana/Cuba 1987 Lect. Notes Math. 1354 106-110
  • [5] Bory Reyes J(1987)The Dini condition and the Cauchy type integral Rev. Cienc. Mat. (Spanish, English summary) 8 9-14
  • [6] Abreu Blaya R(1977)Cauchy integrals on Lipschitz curves and related operators Proc. Natl. Acad. Sci. USA 74 1324-1327
  • [7] Bustamante GJ(1978)Applications of the Cauchy integral on Lipschitz curves Bull. Am. Math. Soc. 84 287-290
  • [8] Bustamante GJ(1982)L’intgrale de Cauchy dfinit un oprateur born sur Ann. Math. (2) 116 361-387
  • [9] Calderón AP(1990) pour les courbes lipschitziennes (French). [The Cauchy integral defines a bounded operator on Colloq. Math. 60/61 601-628
  • [10] Calderón AP(1984) for Lipschitz curves] Ann. Sci. cole Norm. Sup. (4) 17 157-189
123456