Hyperbolic derivatives and generalized Schwarz-Pick estimates

Ghatage, Pratibha; Zheng, Dechao

doi:10.1090/S0002-9939-04-07479-9

Hyperbolic derivatives and generalized Schwarz-Pick estimates
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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.

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