Skip to main content
SpringerLink
Log in

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

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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).

    MATH  MathSciNet  Google Scholar 

  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. L. G. Magnaradze, “On a generalization of the Plemelj-Privalov theorem,”Soobshch. Akad. Nauk Gruz. SSR,8, No. 8, 509–516 (1947).

    MATH  MathSciNet  Google Scholar 

  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).

    MATH  MathSciNet  Google Scholar 

  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).

  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.

  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).

    MathSciNet  Google Scholar 

  8. P. M. Tamrazov,Smoothnesses and Polynomial Approximations [in Russian], Naukova Dumka, Kiev 1975.

    Google Scholar 

  9. O. F. Gerus, “Finite-difference smoothnesses of Cauchy-type integrals,”Ukr. Mat. Zh.,29, No. 5, 642–646 (1977).

    MATH  MathSciNet  Google Scholar 

  10. O. F. Gerus, “Some estimates for moduli of smoothness of Cauchy-type integrals,”Ukr. Mat. Zh.,30, No. 5, 594–601 (1978).

    MATH  MathSciNet  Google Scholar 

  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).

  12. E. M. Dyn’kin, “Smoothness of Cauchy-type integrals,”Zap. Nauch. Sem. LOMI AN SSSR,92, 115–133 (1979).

    MATH  MathSciNet  Google Scholar 

  13. N. A. Davydov, “Continuity of a Cauchy-type integral in a closed domain,”Dokl. Akad. Nauk SSSR,64, No. 6, 759–762 (1949).

    MATH  MathSciNet  Google Scholar 

  14. P. M. Tamrazov, “Contour and solid structural properties of holomorphic functions of complex variable,”Usp. Mat. Nauk,28, No. 1, 131–161 (1973).

    MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. O. F. Gerus
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gerus, O.F. Estimate of the modulus of continuity of a cauchy-type integral in a domain and on its boundary. Ukr Math J 48, 1497–1506 (1996). https://doi.org/10.1007/BF02377818

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02377818

Keywords

Search

Navigation