Busemann Functions and Julia-wolff-carathéodory Theorem for Polydiscs
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چکیده
The classical Julia-Wolff-Carathéodory Theorem is one of the main tools to study the boundary behavior of holomorphic self-maps of the unit disc of C. In this paper we prove a Julia-Wolff-Carathéodory’s type theorem in the case of the polydisc of Cn. The Busemann functions are used to define a class of “generalized horospheres” for the polydisc and to extend the notion of non-tangential limit. With these new tools we give a generalization of the classical Julia’s Lemma and of the Lindelöf Theorem, which the new Julia-Wolff-Carathéodory Theorem relies upon.
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تاریخ انتشار 2007