本项目主要研究Dirichlet空间上的算子与算子代数。与Hardy空间、Bergman空间相比，Dirichlet空间的结构更为复杂，相应的算子与算子代数的结构与性质也复杂得多，一些基本问题都尚未解决。在Hardy空间与Bergman空间上看似平凡的问题，在Dirichlet空间上可能非常复杂，例如乘子的有界性问题在Hardy空间与Bergman空间上是平凡的，但在Dirichlet空间上却是个悬而未决的问题。本项目拟在研究Dirichlet空间上的乘子、Toeplitz算子以及复合算子及其所生成代数的结构与性质。

In this project, we mainly research the operators and operator algebras on Dirichlet space. Compared with the Hardy space and Bergman space, the structure of the Dirichlet space is more complex, and the corresponding structure and properties of their operators and operator algebras are also much more complicated, some basic problems remain to be solved. Some problems seems trivial on Hardy space and Bergman space but can be very complex on Dirichlet space, such as the boundedness of the multipliers, which is trivial on the former two classes spaces, but still an open problem on Dirichlet space. We intend to study the structure and properties of the multipliers, Toeplitz operators and composition operators and their generated algebras on Dirichlet space in this project.