The Julia-Wolff-Caratheodory theorem in polydisks
Complex Variables
2008-02-03 v1
Abstract
The classical Julia-Wolff-Caratheodory theorem gives a condition ensuring the existence of the non-tangential limit of both a bounded holomorphic function and its derivative at a given boundary point of the unit disk in the complex plane. This theorem has been generalized by Rudin to holomorphic maps between unit balls in C^n, and by the author to holomorphic maps between strongly (pseudo)convex domains. Here we describe Julia-Wolff-Caratheodory theorems for holomorphic maps defined in a polydisk and with image either in the unit disk, or in another polydisk, or in a strongly convex domain. One of main tool for the proof is a general version of Lindelof's principle valid for not necessarily bounded holomorphic functions.
Cite
@article{arxiv.math/9612202,
title = {The Julia-Wolff-Caratheodory theorem in polydisks},
author = {Marco Abate},
journal= {arXiv preprint arXiv:math/9612202},
year = {2008}
}