Resumen de Punishing Factors for Finitely Connected Domains

F.G. Avkhadiev, Karl Joachim Wirths

• Let O and ? be two finitely connected hyperbolic domains in the complex plane and let R(z, O) denote the hyperbolic radius of O at z and R(w, ?) the hyperbolic radius of ? at w. We consider functions f that are analytic in O and such that all values f(z) lie in the domain ?. This set of analytic functions is denoted by A(O, ?). We prove among other things that the quantities are finite for all if and only if ?O and ?? do not contain isolated points.