解析函数空间上的算子理论与算子代数是现代数学的重要分支之一，而Volterra积分算子就是其中的一个重要研究对象。因为Volterra积分算子的性质强烈依赖于相应的函数空间，所以在算子理论与函数空间之间建立了密切的联系。解析函数空间的零点集问题，是函数空间的基本问题和难点。并且在研究的过程中发现，零点集与Volterra积分算子有着密切的联系。Besov空间是一类重要的莫比乌斯不变函数空间，其上Volterra积分算子和零点集的研究不够完善。本项目将利用调和分析的方法去研究Besov空间上的Volterra积分算子；并且借助Besov空间的边界刻画及对偶去研究Besov空间的零点集问题。

Operator theory and operator algebra on analytic function space is one of the important branches of modern mathematics, and Volterra integral operator is one of the important research objects. Because the properties of Volterra integral operator strongly depend on the corresponding function space, a close relationship is established between operator theory and function space. The problem of analyzing the set of zeros in function space is the basic problem and difficulty of function space. In the process of research, it is found that the zero set is closely related to Volterra integral operator. Besov space is a kind of important Mobius invariant function space, and the research on Volterra integral operator and zero set is not perfect. In this project, the method of harmonic analysis will be used to study the Volterra integral operator on Besov space; And with the help of the boundary characterization and duality of Besov space, the problem of zero set in Besov space is studied.