理想问题的一个注记

A REMARK ON THE IDEAL PROBLEM

设Ω是Denjoy区域,其边界E满足一致厚条件.本文证明了当η为充分小的正数时,Ω_2(η)的每个连通分支是单连区域,由此,得到若g,f_1,f_2,…f_n∈H~∞(Ω),且|g|≤∑|f_i|,则g^3∈J(f_1,f_2,…f_n).对于无穷个数据的理想问题,本文也指出了相应的结果。

Let Ω be a Denjoy domain,of which the boundary E isuniformly thick. It is proved in the paper that each component of Ω_2(η)is simply connected for η>0 small enough.From Which the authorsshowed that if g,f_1,...f_n∈H~∞(Ω), and|g|≤∑|f_j|, then g^3∈J(f_1,f_2,…f_n).They also point out the corresponding result to the ideal problemfor countably date.