论文标题
在Wiegerinck定理上
On a theorem of Wiegerinck
论文作者
论文摘要
Wiegerinck的一个定理说，$ \ Mathbb C $中任何域上的伯格曼空间都是微不足道的或无限的维度。我们以以下形式概括了该定理。令E为hermitian，holomorphic vector束上$ \ mathbb p^1 $，后来配备了音量表格和$ d $ $ \ mathbb p^1 $中的任意域。然后，$ e $ $ d $的全体形态L2部分的空间要么等于$ h^0（m，e）$，要么具有无限的尺寸。
A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb P^1$, the later equipped with a volume form and $D$ an arbitrary domain in $\mathbb P^1$. Then the space of holomorphic L2 sections of $E$ over $D$ is either equal to $H^0(M,E)$ or it has infinite dimension.
