The Julia-Wolff-Caratheodory theorem in polydisks

Details The Julia-Wolff-Caratheodory theorem in polydisks The Julia-Wolff-Caratheodory theorem in polydisks

1996-12-17

arxiv.org/abs/math/9612202v1

Mathematics

Complex Variables

Scientific paper

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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