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Hyperbolic derivatives and generalized Schwarz-Pick estimates |
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| Authors: | Pratibha Ghatage Dechao Zheng |
| Affiliation: | Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115 ; Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240 |
| 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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