多圆柱上的H^2 Corona问题

H^2 Corona Problem in Polydisc

考虑的是多圆柱上的H2 Corona问题.将多圆柱上的问题转化到单位圆盘上,利用单位圆盘上的H2Hardy空间,定义出一个算子.在证明此算子有界的情况下,利用Hahn-Banach定理及Reize表示找到了方程的解,并且给出了此解的范数估计.

This paper deals with the H^2 Corona problem in the Polydise. The problem of Polydise is transformed into that of unit disk and an operator by H^2 Hardy space is defined in the unit disk. This operator proves bounded, and Hahn-Banaeh Theorem and Reize representation are adopted to solve the equation. Furthermore, the estimate of the solution is given.