本项目拟将调和分析与复分析理论应用于Dirichlet空间理论研究。主要研究奇异积分算子与Dirichlet空间上Carleson测度的关系、拟共形映射诱导的Dirichlet空间上的复合算子及含于Dirichlet空间的边界连续函数组成的代数的理想结构及其在Dirichlet空间循环向量研究中的应用。本项目研究对丰富经典Dirichlet空间算子理论及促进函数空间算子理论在相关学科的应用具有重要意义。

In this project，we intend to study the operator theory on Dirichlet space by means of modern harmonic analysis and complex analysis. We will concern with the relations between singular integral operator and the Carleson measure, the composition operator induced by quasi-conformal mappings, the ideal of algebras consisting of functions in the Dirichlet space which continuous at the closed unit disk and its applications to the characterization of cyclic elements in the Dirichlet space.