论文标题
在半平面上的迪里奇特空间上的构图操作员
Composition Operators on Dirichlet Spaces over the Half-plane
论文作者
论文摘要
随着在单位磁盘的差异空间上进行多项式近似和组成算子的研究，该研究解决了CIMA在1976年提出的问题，本文旨在考虑诸如半平面的无界域的情况。具体而言，我们可以在Dirichlet空间中获得有理近似值，并表征成分算子，该构图操作员在半平面上的Dirichlet空间上具有密集的范围。此外，本文还考虑了半平面上迪利奇的空间与耐寒空间之间的关系。
As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains, such as the half-plane. Specifically, we may obtain the rational approximations in the Dirichlet spaces and characterize the composition operators which has dense range on the Dirichlet spaces over the half-plane. Moreover, this paper also considers the relationship between the Dirichlet spaces and Hardy spaces on half-plane.
