Arkiv för Matematik

  • Ark. Mat.
  • Volume 36, Number 2 (1998), 255-273.

Coefficient estimates for negative powers of the derivative of univalent functions

Daniel Bertilsson

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Letf be a one-to-one analytic function in the unit disc with f′(0)=1. We prove sharp estimates for certain Taylor coefficients of the functions (f′)p, where p<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 of f. We use this to improve known estimates for integral means of the functions |f′|p for integers p⪯−2.

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Ark. Mat., Volume 36, Number 2 (1998), 255-273.

Received: 4 August 1997
First available in Project Euclid: 31 January 2017

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1998 © Institut Mittag-Leffler


Bertilsson, Daniel. Coefficient estimates for negative powers of the derivative of univalent functions. Ark. Mat. 36 (1998), no. 2, 255--273. doi:10.1007/BF02384769.

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