Coefficient estimates for negative powers of the derivative of univalent functions

Daniel Bertilsson Department of Mathematics, Royal Institute of Technology

TBD mathscidoc:1701.332896

Arkiv for Matematik, 36, (2), 255-273, 1997.8
Let$f$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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@inproceedings{daniel1997coefficient,
  title={Coefficient estimates for negative powers of the derivative of univalent functions},
  author={Daniel Bertilsson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203553618015705},
  booktitle={Arkiv for Matematik},
  volume={36},
  number={2},
  pages={255-273},
  year={1997},
}
Daniel Bertilsson. Coefficient estimates for negative powers of the derivative of univalent functions. 1997. Vol. 36. In Arkiv for Matematik. pp.255-273. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203553618015705.
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