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

Author： Plaksa S.  

Publisher： Springer Publishing Company

ISSN： 0041-5995

Source： Ukrainian Mathematical Journal, Vol.57, Iss.2, 2005-02, pp. : 261-270

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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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