模空间上的截断Toeplitz算子和截断Hankel算子具有丰富的内涵，既包含Toeplitz矩阵、Hankel矩阵又包含Volterra积分算子、Sz-Nagy-Foias压缩算子模型。我们用Hardy空间上的Hankel算子理论和函数代数等相关技巧解决了有界符号的截断Toeplitz算子的紧性。本项目将继续沿着这个思路并且综合利用复分析、调和分析和泛函分析的相关技巧，研究模空间上的截断Toeplitz算子和截断Hankel算子的有界性和紧性等问题。

Truncated Toeplitz operators and truncated Hankel operators on model spaces contain not only Toeplitz matrices、Hankel matrices but also Volterra integral operator、 Sz-Nagy-Foias model operator for contractions. We solved the compactness of truncated Toeplitz operators on model spaces by the techniques of theory of Hankel operators on Hardy space and function algebras. This project will continue to follow this idea and use the techniques of complex analysis, harmonic analysis and functional analysis to study the problem on boundedness and compactness of truncated Toeplitz operators and truncated Hankel operators on model spaces.