Hyperbolic derivatives and generalized Schwarz-Pick estimates
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- by Pratibha Ghatage and Dechao Zheng PDF
- Proc. Amer. Math. Soc. 132 (2004), 3309-3318 Request permission
Abstract:
In this paper we use the beautiful formula of Faa di Bruno for the $n$th derivative of composition of two functions to obtain the generalized Schwarz-Pick estimates. By means of those estimates we show that the hyperbolic derivative of an analytic self-map of the unit disk is Lipschitz with respect to the pseudohyperbolic metric.References
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Additional Information
- Pratibha Ghatage
- Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
- Email: p.ghatage@csuohio.edu
- Dechao Zheng
- Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- MR Author ID: 229147
- Email: zheng@math.vanderbilt.edu
- Received by editor(s): July 9, 2003
- Received by editor(s) in revised form: August 12, 2003
- Published electronically: May 12, 2004
- Additional Notes: The second author was supported in part by the National Science Foundation.
- Communicated by: Joseph A. Ball
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3309-3318
- MSC (2000): Primary 30C80
- DOI: https://doi.org/10.1090/S0002-9939-04-07479-9
- MathSciNet review: 2073307