多圆盘中的Julia-Wolff-Caratheodory定理
The Julia-Wolff-Caratheodory theorem in polydisks
摘要：
经典的Julia-Wolff-Caratheodory定理给出了有界全纯函数及其导数在复平面上单位圆的给定边界点处存在非切向极限的条件. Rudin把这个定理推广到了C^n中单位球之间的全纯映射，作者也把它推广到了强（伪）凸区域之间的全纯映射。本文给出了定义在多圆盘上的全纯映射的Julia-Wolff-Caratheodory定理，其象要么在单位圆盘上，要么在另一个多圆盘上，要么在强凸区域上.证明的主要工具之一是对未必有界的全纯函数有效的Lindelof原理的一般形式。
英文摘要：
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.
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