加权Dirichlet空间D_φ~2上的复合算子

Composition Operators on the Weighted Dirichlet Space with Exponential Type Weights

设D是复平面中单位圆盘,φ:D→R是一个次调和函数,D2φ是D上的加权Dirichlet空间.对某类次调和函数φ,文章研究了D2φ上的复合算子Cψ,分别得到了Cψ为D2φ上的有界、紧、Schattenp-类算子的特征.

Let φ:D→R be a subharmonic function on the unit disk D in the complex plane and D^2_φ denote the weighted Dirichlet space with exponential type weights on D. For some class of subharmonic functions φ, we characterize the boundedness, compactness and Schatten class of composition operators on D^2_φ.