加权Bergman空间的若干逼近定理

Some Approximation Theorems of Weighted Bergman Space

摘要:

设H2（Ω,φ）为区域Ω上相对于权φ的Bergman空间.给出若Ω为有限个Carathéodory区域之交且φ在Ω-次调和，那么Ω-上的全纯函数在H2（Ω，φ)中稠密，证明了当Ω=Cn且φ是近似圆形时，多项式在H2（Ω,φ)中稠密.

Abstract:

Let H2(Ω,φ) be the Bergman space with respect to φ on the domain Ω. It is proved that holomorphic functions on Ω are dense in H2(Ω,φ) when Ω is the intersection of a finite number of Carathéodory domains and φ is a subharmonic function on Ω. If Ω = Cn and φ is approximately circular polynomials are dense in H2(Ω,φ).