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

• Datum: 2005
• Hauptverfasser: Plaksa, S. A., Плакса, С. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2005
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3589
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.