Schwarz-Pick Inequalities for Hyperbolic Domains in the Extended Plane |
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| Authors: | Farit G Avkhadiev Karl-Joachim Wirths |
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| Institution: | (1) Chebotarev Research Institute, Kazan State University, R-, 420008 Kazan, Russia;(2) Institut für Analysis, Technische Universität, D-, 38106 Braunschweig, Germany |
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| Abstract: | Let  and  be two hyperbolic simply connected domains in the extended complex plane C¯ = C¯  { }. We derive sharp upper bounds for the modulus of the nth derivative of a holomorphic, resp. meromorphic function f:  at a point z
0  . The bounds depend on the densities  (z
0) and (f(z
0)) of the Poincaré metrics and on the hyperbolic distances of the points z
0 and f(z
0) to the point . |
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| Keywords: | Poincaré metric hyperbolic distance derivatives holomorphic function |
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