Skip to main content
SpringerLink
Log in

Integral means, univalent functions and circular symmetrization

  • Published:
Acta Mathematica

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

References

  1. Baernstein, A., Proof of Edrei's spread conjecture.Proc. London Math. Soc., (3) 26 (1973), 418–434.

    MATH  MathSciNet  Google Scholar 

  2. Baernstein, A., A generalization of the cos πϱ Theorem. To appear inTrans. Amer. Math. Soc.

  3. Baernstein, A., Functions extremal for the spread relation. To appear.

  4. Bazilevic, I. E., On distortion theorems and coefficients of univalent functions (Russian),Mat. Sb. N.S., 28 (70) (1951), 147–164.

    MATH  MathSciNet  Google Scholar 

  5. Borell, C., An inequality for a class of harmonic functions inn-space. Preprint.

  6. Duren, P. &Schiffer, M., A variational method for functions schlicht in an annulus.Arch. Ratinal Mech. Anal., 9 (1962), 260–272.

    MathSciNet  MATH  Google Scholar 

  7. Fitzgerald, C. H., Quadratic inequalities and coefficient estimates for schlicht functions.Arch. Rational Mech. Anal., 46 (1972), 356–368.

    Article  MATH  MathSciNet  Google Scholar 

  8. Groetzsch, H., Über einige Extremalprobleme der konformen Abbildung.Leipzig, Berichte, 80 (1928), 367–376.

    MATH  Google Scholar 

  9. Haliste, K., Estimates of harmonic measures.Ark. Mat., 6 (1965), 1–31.

    MATH  MathSciNet  Google Scholar 

  10. Hardy, G. H., Littlewood, J. & Pólya, G.,Inequalities, Cambridge, 1959.

  11. Hayman, W. K., Some applications of the transfinite diameter to the theory of functions.J. Anal. Math., 1 (1951), 155–179.

    MATH  MathSciNet  Google Scholar 

  12. Hayman, W. K.,Multivalent Functions. Cambridge, 1967.

  13. Hayman, W. K.,Research Problems in Function Theory. London, 1967.

  14. Hille, E.,Analytic Function Theory, Vol. II. Boston, 1962.

  15. Jenkins, J. A., On circularly symmetric functions.Proc. Amer. Math. Soc., 6 (1955), 620–624.

    Article  MATH  MathSciNet  Google Scholar 

  16. Jenkins, J. A. Univalent Functions and Conformal Mapping. Berlin-Göttingen-Heidelberg, 1958.

  17. Lehto, O., A majorant principle in the theory of functions.Math. Scand., 1 (1953).

  18. Lohwater, A. J., Piranian, G. &Rudin, W., The Derivative of a schlicht function.Math. Scand., 3 (1955), 103–106.

    MathSciNet  MATH  Google Scholar 

  19. MacGregor, T. H., Applications of extreme-point theory to univalent functions.Michigan Math. J., 19 (1972), 361–376.

    Article  MATH  MathSciNet  Google Scholar 

  20. Netanyahu, E., On univalent functions in the unit disk whose image contains a given disk.J. Anal. Math., 23 (1970), 305–322.

    Article  MATH  MathSciNet  Google Scholar 

  21. Nevanlinna, R.,Analytic Functions. Berlin-Heidelberg-New York, 1970.

  22. Pólya, G. & Szegö, G.,Isoperimetric Inequalities in Matematical Physics. Princeton, 1951.

  23. Ohtsuka, M.,Dirichlet Problem, Extremal Length, and Prime Ends. New York, 1970.

  24. Rado, T.,Subharmonic Functions. Berlin, 1937.

  25. Spencer, D. C., On mean one-valent functions.Ann. of Math. (2) 42 (1941).

  26. Wilken, D. R., The integral means of close-to-convex functions.Michigan Math. J., 19 (1972), 377–379.

    Article  MATH  MathSciNet  Google Scholar 

  27. Kirwan, B. & Schober, G., Integral means for univalent functions in an annulus. University of Maryland Technical Report, 1974.

Download references

Author information

Authors and Affiliations

  1. Washington University, St. Louis, Mo., USA

    Albert Baernstein II

Authors
  1. Albert Baernstein II
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by NSF Grant GP-38959

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baernstein, A. Integral means, univalent functions and circular symmetrization. Acta Math. 133, 139–169 (1974). https://doi.org/10.1007/BF02392144

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392144

Keywords

Search

Navigation