多复变数全纯映射精细的Bohr定理

Refined Bohr’s theorem for holomorphic mappings in several complex variables

本文首先建立不依赖自同构从复Banach空间平衡域到Cn单位多圆柱上一定限制条件下全纯映射精细的范数型Bohr定理及复Banach空间X上单位球到复Banach空间Y上单位球全纯映射精细的泛函型Bohr定理.其次,给出有界对称域上全纯映射精细的Bohr定理.最后,得到J*代数单位球上全纯映射精细的Bohr定理.所得结果将一维的Bohr定理推广至高维.

In this paper, we first establish the refined Bohr’s theorem of norm type for holomorphic mappings from the balanced domain in complex Banach spaces to the unit polydisk in Cnunder some restricted conditions and the refined Bohr’s theorem of functional type for holomorphic mappings from the unit ball in one complex Banach space X to the unit ball in another complex Banach space Y without any holomorphic automorphism.Secondly, we get the refined Bohr’s theorem for holomorphic mappings on bounded symmetric domains. We also obtain the refined Bohr’s theorem for holomorphic mappings on the unit ball of a J*-algebra. Our results extend Bohr’s theorem from one dimension to higher dimensions.