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Hyperbolic derivatives and generalized Schwarz-Pick estimates
Author(s):
Pratibha
Ghatage;
Dechao
Zheng
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3309-3318.
MSC (2000):
Primary 30C80
Posted:
May 12, 2004
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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:
10.1090/S0002-9939-04-07479-9
PII:
S 0002-9939(04)07479-9
Received by editor(s):
July 9, 2003
Received by editor(s) in revised form:
August 12, 2003
Posted:
May 12, 2004
Additional Notes:
The second author was supported in part by the National Science Foundation.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2004,
American Mathematical Society
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