Israel Journal of Mathematics

, Volume 17, Issue 1, pp 105–107 | Cite as

Integral means of analytic functions

  • Bernard Pinchuk


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.


Analytic Function Harmonic Function Convex Function Unit Disc Univalent Function 


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  1. 1.
    A. Baernstein,Integral means of univalent functions, Notices Amer. Math. Soc.20 (1973), A-613.Google Scholar
  2. 2.
    A. Beurling,Etudes sur un problème de majoration, Thèse pour le doctorat, Upsal, 1933.Google Scholar
  3. 3.
    P. Duren,Theory of H p spaces, Academic Press, New York, 1970.MATHGoogle Scholar
  4. 4.
    W. Hayman,Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48 Cambridge University Press, Cambridge, 1958.MATHGoogle Scholar

Copyright information

© Hebrew University 1974

Authors and Affiliations

  • Bernard Pinchuk
    • 1
  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael

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