Abstract
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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 476–484, April, 1998.
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Gerus, O.F. On the modulus of continuity of solid derivatives of a Cauchy-type integral. Ukr Math J 50, 539–549 (1998). https://doi.org/10.1007/BF02487386
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DOI: https://doi.org/10.1007/BF02487386