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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
Article

Abstract

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.

Keywords

Analytic Function Unit Disc Univalent Function Coefficient Estimate Sharp Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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