Some Properties of the Integral of Cauchy Type for Two Complex Variables at the Points of the Contour

In the complex analysis the singular integral of Cauchy-type at the point of the curve of integration is defined as a sum of the logarithmic part and of the rest F. In particular F is the convergent integral if the function under of a sign of the integral is of the Holder-type. In this paper the new definition of F and its derivatives is introduced. Some analytic properties of F in the case of two complex variables are studied. In the second part of the paper the generalization of the Fock-Kuni theorem on two complex variables is proved. We propose to use the Fock-Kuni theorem to examine the above-mentioned function F.