Ukrainian Mathematical Journal

, Volume 48, Issue 10, pp 1497–1506 | Cite as

Estimate of the modulus of continuity of a cauchy-type integral in a domain and on its boundary

  • O. F. Gerus


We estimate the modulus of continuity of a Cauchy-type integral in a closed domain and its limit values on the boundary in the case where the boundary of the domain is an arbitrary closed rectifiable Jordan curve.


Holomorphic Function Arbitrary Point Closed Curve Singular Integral Equation Absolute Constant 
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  1. 1.
    V. V. Salaev, “Direct and inverse estimates for a singular Cauchy integral along a closed curve,”Mat. Zametki,19, No. 3, 365–380 (1976).zbMATHMathSciNetGoogle Scholar
  2. 2.
    A. Zygmund, “Sur le module continuite de la serie conjuguee de la serie de Fourier,”Pr. Mat.-Fiz.,33, 125–132 (1924).Google Scholar
  3. 3.
    L. G. Magnaradze, “On a generalization of the Plemelj-Privalov theorem,”Soobshch. Akad. Nauk Gruz. SSR,8, No. 8, 509–516 (1947).zbMATHMathSciNetGoogle Scholar
  4. 4.
    L. G. Magnaradze, “On a generalization of the Privalov theorem and its application to some linear boundary-value problems in the theory of functions and to singular integral equations,”DokL Akad. Nauk SSSR,68, No. 4, 657–660 (1949).zbMATHMathSciNetGoogle Scholar
  5. 5.
    A. A. Babaev, “On a singular integral with continuous density,”Uchen. Zap. Azerb. Univ., Ser. Fiz.-Mat. Khim. Nauk, No. 5, 11–28 (1965).Google Scholar
  6. 6.
    P. M. Tamrazov, “On limited holomorphic functions in a complex domain,” in:Proceedings of the Third Congress of Bulgarian Mathematicians. Part 1, Varna (1972), pp. 186–187.Google Scholar
  7. 7.
    A. A. Babaev and V. V. Salaev, “One-dimensional singular operator with continuous density along a closed curve,”Dokl. Akad. Nauk SSSR,209, No.6, 1257–1260 (1973).MathSciNetGoogle Scholar
  8. 8.
    P. M. Tamrazov,Smoothnesses and Polynomial Approximations [in Russian], Naukova Dumka, Kiev 1975.Google Scholar
  9. 9.
    O. F. Gerus, “Finite-difference smoothnesses of Cauchy-type integrals,”Ukr. Mat. Zh.,29, No. 5, 642–646 (1977).zbMATHMathSciNetGoogle Scholar
  10. 10.
    O. F. Gerus, “Some estimates for moduli of smoothness of Cauchy-type integrals,”Ukr. Mat. Zh.,30, No. 5, 594–601 (1978).zbMATHMathSciNetGoogle Scholar
  11. 11.
    T. S. Salimov, “Direct estimate for a singular Cauchy integral,”Nauch. Tr. MV SSO Azerb. SSR, Ser. Fiz.-Mat. Nauk, No. 5, 59–75 (1979).Google Scholar
  12. 12.
    E. M. Dyn’kin, “Smoothness of Cauchy-type integrals,”Zap. Nauch. Sem. LOMI AN SSSR,92, 115–133 (1979).zbMATHMathSciNetGoogle Scholar
  13. 13.
    N. A. Davydov, “Continuity of a Cauchy-type integral in a closed domain,”Dokl. Akad. Nauk SSSR,64, No. 6, 759–762 (1949).zbMATHMathSciNetGoogle Scholar
  14. 14.
    P. M. Tamrazov, “Contour and solid structural properties of holomorphic functions of complex variable,”Usp. Mat. Nauk,28, No. 1, 131–161 (1973).zbMATHMathSciNetGoogle Scholar

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© Plenum Publishing Corporation 1997

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  • O. F. Gerus

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