Busemann Functions and Julia-Wolff-Caratheodory Theorem for Polydiscs
Chiara Frosini
Abstract
The classical Julia-Wolff-Caratheodory Theorem is one of the main tools to study the boundary behavior of holomorphic self-maps of the unit disc of . In this paper we prove a Julia-Wolff-Caratheodory's type theorem in the case of the polydisc of n. 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 Lindelof Theorem, which the new Julia-Wolff-Caratheodory Theorem relies upon.
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