A Necessary and Sufficient Condition for the Existence of a Singular Integral with Cauchy Kernel

Ioseb D. Machavariani

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

Abstract:

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.

Pages: 153 – 159 | Full PDF Paper