Abstract

Let f : Ω → Ω be a holomorphic mapping, where Ω is one of the four classical domains in C^m×n. We show that, if P = f(0), we have

for ∥Z∥_Ω < and φ_P in Aut Ω such that φ_P(P) = 0. This generalizes to higher dimensions a classical result of Bohr, which corresponds to the case Ω = {z : |z| < 1}⊂ C. The constant is the best possible.

Keywords

holomorphic mapping, homogeneous expansion, classical domains, Bohr's theorem

Mathematical Subject Classification

Primary: 30H05

Secondary: 32A05

Milestones

Received: 23 December 2005
Revised: 25 September 2006
Accepted: 26 October 2006

Authors