Singular integral operators with generalized Cauchy kernel on piecewise smooth contour

Singular integral operators of two types are considered on a piecewise smooth contour in weighted Lebesgue spaces with generalized Cauchy kernels, related to the parametrix elliptic systems first order plane. The type linear over field complex numbers and represented as usual combination singular operator multiplication by continuous matrix functions. second act space real vector functions and, thus, R. They arise direct reduction boundary problems using representations. A criterion is obtained for these be Fredholm, formula their index indicated.