English

Busemann Functions and Julia-Wolff-Caratheodory Theorem for Polydiscs

Complex Variables 2007-05-23 v1

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 \C\C. In this paper we prove a Julia-Wolff-Caratheodory's type theorem in the case of the polydisc of \Cn.\C^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.

Keywords

Cite

@article{arxiv.math/0702581,
  title  = {Busemann Functions and Julia-Wolff-Caratheodory Theorem for Polydiscs},
  author = {Chiara Frosini},
  journal= {arXiv preprint arXiv:math/0702581},
  year   = {2007}
}