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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Hyperbolic derivatives and generalized Schwarz-Pick estimates

Authors: Pratibha Ghatage and Dechao Zheng
Journal: Proc. Amer. Math. Soc. 132 (2004), 3309-3318
MSC (2000): Primary 30C80
Published electronically: May 12, 2004
MathSciNet review: 2073307
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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.

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Additional Information

Pratibha Ghatage
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

Dechao Zheng
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

PII: S 0002-9939(04)07479-9
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
Article copyright: © Copyright 2004 American Mathematical Society