函数空间是现代数学的一个重要研究方向，它本身具有非常丰富而成熟的理论系统，在纯数学与应用分析领域都有着深刻影响。为了进一步丰富该理论在其他领域的应用，本项目将探讨它在BMO-Teichmüller空间理论方面的应用，这也是Teichmüller理论的一个重要研究课题。.. 本项目将进行以下三方面的研究：（1）利用调和分析手段研究BMO/VMO-Teichmüller空间；（2）Carleson测度等方法在高维解析函数空间上的应用；（3）有限维Teichmüller空间的研究及其应用。.. 本项目是访学合作项目，通过对函数空间理论在Teichmüller理论的应用研究，将申请人非常熟悉的解析函数空间理论和参与人的研究领域Teichmüller理论进行深入结合，从某种意义上，属于交叉领域研究课题，具有非常重要的研究价值。

Function space is an important research topic of modern mathematics. It has a very rich and mature theoretical system and has a profound influence in the fields of pure mathematics and applied analysis. In order to enrich the application of this theory in other research fields, this project will explore its application in BMO Teichmüller space theory, which is also an important research topic of Teichmüller theory.. .Concretely, the research plan consists of：(1) study on BMO / VMO-Teichmüller space by using harmonic analysis; (2) the application of Carleson measure in high-dimensional analytical functions space; (3) research on the finite-dimensional Teichmüller space. . .This project is a visiting cooperation project. It hopes that, through the application research of function space theory in Teichmüller theory, aim to deeply combine the analytical function space theory familiar to the applicant, and the Teichmuller theory which is the research field of the participant. In some sense, this project belongs to the cross-field research topic, which has very important theoretical research value.