解析函数空间及其上的算子理论一直备受关注，这是因为它在经典分析和近代算子理论与算子代数之间建立起了联系，从而为两方面的研究提供了新的视角和工具。复合算子、Hilbert算子是其中两类重要算子。本项目致力于研究解析函数空间上的复合算子、加权复合算子的差分与广义Hilbert算子。主要从以下三个方面研究：(1)研究单位圆盘上Bloch型空间上加权复合算子的差分的性质; (2)考虑单位圆盘上一些解析函数空间在Bloch空间的闭包的等价刻画以及其上的复合算子的有界性和紧性问题; (3)研究单位圆盘上一些解析函数空间(如：Bergman空间、Dirichlet空间、Bloch空间和Besov空间等)上的广义Hilbert算子的性质。

The operator theory on the analytic function spaces has been attracting much attention in the current functional analysis and complex analysis. Because it builds the connection between classcial analysis and modern operator theory and operator algebra. Thus it provides a new tool and perspective for the research in the above two aspects. Composition operator and Hilbert operator are two important operators in this field. In this project, we will focus on the study of the following three parts: (1)Differences of weighted composition operators on the Bloch type spaces；(2)Composition operator and closures of some analytic function spaces in the Bloch space；(3)Generalized Hilbert operators on some analytic function spaces.