Once Again About the Cauchy Type Integral

Ioseb D. Machavariani

Muskhelishvili Institute of Computational Mathematics of the Georgian Technical University, 0159 Tbilisi, Georgia.

Abstract:

In this article it is shown that the expression considered in the articles [1,2,4], called by A.P. Calderon the Cauchy operator has nothing in common with the classical Cauchy operator and the results of the above works are erroneously formulated. We indicate a geometric condition on the rectifiable Jordan curve Γ whose fulfilment is necessary and sufficient for the existence of finite angular boundary values and a Cauchy type integral of summable density for almost all points of the curve Γ.

Keywords: singular integral, Cauchy kernel.

Pages: 16 – 25 | Full PDF Paper