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

DOI:
https://doi.org/10.1090/S0002-9939-04-07479-9

Published electronically:
May 12, 2004

MathSciNet review:
2073307

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we use the beautiful formula of Faa di Bruno for the 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

Email:
p.ghatage@csuohio.edu

**Dechao Zheng**

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

Email:
zheng@math.vanderbilt.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07479-9

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