本项目利用现代分析的理论和方法，继续深入研究近年来十分活跃的一些新型函数空间（特别是QK空间等）中的若干重要问题。具体包括：研究Morrey空间与QK空间的本质联系，并以此发现QK空间的深刻背景，为在偏微分方程中的应用提供理论和方法；研究万有Teichmuller空间与一般QK空间之间的内在关系，给出QK-Teichmuller空间的特征；研究高维（实和复）QK空间的特征，建立高维QK空间的基本理论；研究Fock 空间的特征及相关的算子理论。力争攻克一些有关QK空间及相关问题中尚未解决的问题。通过本项目的研究，期望能进一步丰富和发展QK空间理论，并寻求其可能的应用。

Using the theory and method of modern analysis, some important problems in some new function spaces (especially QK space) which are very active in recent years will be investigated in this proposal. By studying the relationship between Morrey space and QK space, find the profound background of the QK space and its applications in PDE; show the intrinsic relationship between universal Teichmuller space and QK space and give characterizations of QK-Teichmuller space; built the basic theory of high dimensional (real and complex) QK spaces; characterize Fock space and related operator theory problems. Through our research, we hope to overcome some open questions on QK space, to develop the theory of QK space, and to seek the possibility of applications.