Skip to main content
SpringerLink
Log in

Integral means of analytic functions

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Sharp bounds for general integral means of analytic functions in the unit disc are determined. These bounds depend only on the moduli of the points on the boundary of the image domain nearest to and farthest from the origin. The proof is shown to be a simple application of a deep theorem of A. Beurling in potential theory.

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. A. Baernstein,Integral means of univalent functions, Notices Amer. Math. Soc.20 (1973), A-613.

    Google Scholar 

  2. A. Beurling,Etudes sur un problème de majoration, Thèse pour le doctorat, Upsal, 1933.

  3. P. Duren,Theory of H p spaces, Academic Press, New York, 1970.

    MATH  Google Scholar 

  4. W. Hayman,Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48 Cambridge University Press, Cambridge, 1958.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel

    Bernard Pinchuk

Authors
  1. Bernard Pinchuk
    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

Pinchuk, B. Integral means of analytic functions. Israel J. Math. 17, 105–107 (1974). https://doi.org/10.1007/BF02756831

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02756831

Keywords

Search

Navigation