多圆柱上的H2 Corona问题

H2 Corona Problem in Polydisc

摘要:

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H2 Hardy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(e) -方程的解,并且给出了此解的范数估计.

关键词:H2 Corona问题;格林公式;多圆柱;多圆柱;Corona;问题;Polydisc;范数估计;方程的解;定理;情况;算子有界;空间;Hardy;利用;单位圆盘;转化

Abstract:

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.

Key words:H2 Corona问题;格林公式;多圆柱;多圆柱;Corona;问题;Polydisc;范数估计;方程的解;定理;情况;算子有界;空间;Hardy;利用;单位圆盘;转化