Lipschitz函数空间的分解及其应用

本项目将Banach空间非线性几何与粗几何有机结合来研究度量空间，特别是Banach空间上的嵌入理论以及Lipschitz函数空间的结构，具体研究内容如下：.（1）通过建立相应于粗Lipschitz嵌入的万有粗稳定性不等式来研究度量空间的粗稳定性；.（2）研究Lipschitz函数空间的分解及其某些子空间和商的特殊结构和性质，例如：研究超滤子-逼近正齐次标准Lipschitz函数空间的相关结构和性质；.（3）研究Lindenstrauss问题：Banach空间是否是其二次对偶空间的Lipschitz收缩。

In this project, we combine nonlinear geometry of Banach spaces with coarse geometry to study metric spaces, especially the embedding theory on Banach spaces and the structure of Lipschitz function spaces. The specific research aspects are as follows.(1) By establishing the universal coarse stability inequality corresponding to coarse Lipschitz embedding, the coarse stability of metric spaces is studied;.(2) we study the decomposition of Lipschitz function space and the special structures and properties of some subspaces and quotients. For example, we study the related structures and properties of ultrafilter-approximately positively homogeneous and standard Lipschitz function space;.(3) we study the Lindenstrauss problem: whether a Banach space is a Lipschitz retract of its second dual space.