Arkiv för Matematik

, Volume 36, Issue 2, pp 255–273 | Cite as

Coefficient estimates for negative powers of the derivative of univalent functions

  • Daniel Bertilsson


Letf be a one-to-one analytic function in the unit disc withf′(0)=1. We prove sharp estimates for certain Taylor coefficients of the functions(f′) p , wherep<0. The proof is similar to de Branges’ proof of Bieberbach’s conjecture, and thus relies on Löwner’s equation. A special case leads to a generalization of the usual estimate for the Schwarzian derivative off. We use this to improve known estimates for integral means of the functions |f′| p for integersp⪯−2.


Analytic Function Unit Disc Univalent Function Coefficient Estimate Sharp Estimate 
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Copyright information

© Institut Mittag-Leffler 1998

Authors and Affiliations

  • Daniel Bertilsson
    • 1
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden

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