Skip to main content
SpringerLink
Log in

Remarks on a parametric representation of Nevanlinna-Dzhrbashyan classes

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

This article presents a parametric representation for classes of functions f that are holomorphic in the unit disk and such that

$$\int_{|\zeta |< 1} {(1 - |\zeta |)^{\alpha - 1} \log ^ + } |f(\zeta )|dm_2 (\zeta )< + \infty (\alpha > 0).$$

Here m2 is the flat Lebesque measure.

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

Literature cited

  1. M. M. Dzhrbashyan, “On canonical representation of functions that are meromorphic in the unit disk,” Dokl. Akad. Nauk Arm. SSR,3, No. 1, 3–9 (1945).

    Google Scholar 

  2. M. M. Dzhrbashyan, “On the problem of representing analytic functions,” Soobshch. Inst. Mat. Mekh., Akad. Nauk Arm. SSR, No. 2, 3–40 (1948).

    Google Scholar 

  3. M. M. Dzhrbashyan, “On parametric representation of certain general classes of meromorphic functions in the unit disk,” Dokl. Akad. Nauk SSSR,157, No. 5, 1024–1027 (1964).

    Google Scholar 

  4. M. M. Dzhrbashyan, Integral Transforms and Representation of Functions in a Complex Domain [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  5. R. Nevanlinna, Single-Valued Analytic Functions [in Russian], Gostekhizdat, Moscow-Leningrad (1941).

    Google Scholar 

  6. F. A. Shamoyan, “Parametric representation of classes of functions that are holomorphic in the unit disk and can grow close to the boundary,” in: Proc. National Conf. on Methods for Presenting Mathematics and Mechanics in the Higher Schools [in Russian], Erevan (1986).

  7. A. E. Djrbashian and F. A. Shamoian, Topics in the Theory of AαP Spaces, Teubner, Leipzig (1988).

    Google Scholar 

  8. E. M. Stein, Singular Integrals and the Differential Properties of Functions [Russian translation], Mir, Moscow (1973).

    Google Scholar 

  9. P. L. Duren, Theory of HP Spaces, Academic Press, New York (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematics, Armenian Academy of Sciences, USSR

    F. A. Shamoyan

Authors
  1. F. A. Shamoyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 128–140, July, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shamoyan, F.A. Remarks on a parametric representation of Nevanlinna-Dzhrbashyan classes. Math Notes 52, 727–737 (1992). https://doi.org/10.1007/BF01247657

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01247657

Keywords

Search

Navigation