On the Derivatives of Cauchy-Type Integrals in the Polydisk

摘要

In the paper the formulas are provided for the derivatives of Cauchy-type integral K[u] which are smooth on the skeleton of the polydisk of functions u. These formulas express the derivatives of the order m of K[u] through the derivatives of lower order (Theorem 2.1). They are used for estimating the smoothness of the derivatives of the Cauchy-type integral in terms of Holder order scale (Theorem 3.1).