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Busemann Functions and the Julia–Wolff–Carathéodory Theorem for polydiscs
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Chiara Frosini
Published/Copyright:
April 13, 2010
Abstract
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 type theorem in the case of the polydisc of 
. 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 Lemma and of the Lindelöf Theorem, which the new Julia–Wolff–Carathéodory Theorem relies upon.
Key words.: Holomorphic maps; boundary behavior
Received: 2008-02-29
Revised: 2008-06-04
Published Online: 2010-04-13
Published in Print: 2010-July
© de Gruyter 2010
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