Abstract
In a domain bounded by a closed rectifiable Jordan curve, we obtain estimates for the modulus of a Cauchy-type integral and its derivatives in terms of the contour moduli of smoothness of the integrand and a metric characteristic of the curve.
Similar content being viewed by others
References
P. M. Tamraroz,Smoothnesses and Polynomial Approximations [in Russian], Naukova Dumka, Kiev (1975).
P. M. Tamrazov,Finite-Difference Smoothnesses and Polynomial Approximations [in Russian], Preprint No. 75-10 Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1975).
P. M. Tamrazov, “Finite-difference smoothnesses and approximation”, in:Colloq. Math. Soc. Janos Bolyai, 19. Fourier Analysis and Approximation Theory, Budapest (1976), pp. 827–843.
N. I. Muskhelishvili,Singular Integral Equations [in Russian], Nauka, Moscow (1968).
O. F. Gerus, “Estimate of the modulus of continuity of a Cauchy-type integral in a domain and on its boundary,”Ukr. Mat. Zh. 48, No. 10, 1321–1328 (1996).
A. O. Gel'fond,Finite-Difference Calculus [in Russian], Nauka, Moscow (1967).
Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 732–743, June, 1999.
Rights and permissions
About this article
Cite this article
Gerus, O.F. Estimates for the modulus of a Cauchy-type integral and its derivatives. Ukr Math J 51, 813–826 (1999). https://doi.org/10.1007/BF02591970
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02591970