Differentiation of Singular Integrals with Piecewise-Continuous Density and Boundary Values of Derivatives of a Cauchy-Type Integral

Abstract

We establish sufficient conditions for the differentiability of a singular Cauchy integral with piecewise-continuous density. Formulas for the nth-order derivatives of a singular Cauchy integral and for the boundary values of the nth-order derivatives of a Cauchy-type integral are obtained.