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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 222–229, February, 2005.
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Plaksa, S.A. Differentiation of Singular Integrals with Piecewise-Continuous Density and Boundary Values of Derivatives of a Cauchy-Type Integral. Ukr Math J 57, 261–270 (2005). https://doi.org/10.1007/s11253-005-0186-7
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DOI: https://doi.org/10.1007/s11253-005-0186-7