Banach空间中的嵌入理论及其应用

Banach空间中的嵌入问题一直是泛函分析研究的一个重要问题，其研究成果广泛应用于数学其它分支（如：偏微分方程理论）、经济和工程技术等领域。本项目致力于加强和发展嵌入问题的理论研究及其应用，将嵌入理论及其应用中的经典分析方法与我们研究嵌入问题和应用于解决微分方程问题上所建立的方法（例如：傅立叶乘子的方法）有机结合起来，旨在探讨和解决如下问题： .(1) 特殊度量空间嵌入超自反空间的特征和充分条件；.(2) 嵌入理论在算子值傅立叶乘子理论及微分方程中的应用。

The embedding problem is always an important problem in functional analysis，and the results about it are widely applied in many fields such as other branches of mathematics ( for instance, the theory of partial differential equations ), economics and engineering technology. This program devotes to strengthening and developing its theoretical research and applications. .We will combine the classical analysis methods in the embedding theory and its applications with the methods established on solving the embedding problems and the problems of differential equations ( for instance, Fourier multiplier methods) to consider the following problems:.(1) The characterizations and sufficient conditions of special metric spaces which can be embedded into superreflexive spaces;.(2) The applications of embedding theory on operator-valued Fourier multiplier theory and differential equations.