On the modulus of continuity of solid derivatives of a Cauchy-type integral

We establish sufficient conditions for the existence of solid derivatives of a continuous extension of a Cauchy-type integral onto the closure of a domain and obtain an estimate for the moduli of continuity of these derivatives. We prove that the Newton-Leibniz formula is true for certain classes of Jordan rectifiable curves. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 476–484, April, 1998.