加权Fock空间上的Toeplitz算子和Hankel算子的基本性质

加权Fock空间是Fock空间和经典Sobolev空间相结合的产物。目前加权Fock空间研究是函数空间结构理论的热点问题之一. 本项目拟推广Fock空间的Toeplitz算子和Hankel算子的基本性质，并研究加权Fock空间的空间结构. 具体地：.1) 研究分数阶Fock-Sobolev空间上具有非负可测符号Toeplitz算子的有界性, 紧性和Schatten p类. .2) 研究在Fock型空间上具有非负可测符号Toeplitz算子的有界性, 紧性和Schatten p类. .3) 研究(向量值)分数阶Fock-Sobolev空间上具有有界符号Hankel算子的基本性质..4) 研究权为e^{-|z|^m}的加权Fock空间上Haplitz算子和Hankel算子乘积的基本性质..以上都是全纯空间上的算子理论和算子代数理论的基本内容，具有较好的理论价值和研究意义.

The weighted Fock Space is the combination of structures of the Fock space and Sobolev space, whose research is the one of hot topics in the study of theory of function space at present. In this proposal, we focus our attentions on generalizing the properties of Toeplitz operators and Hankel operators on the weighted Fock space and observing their structures. The details are described as follows:.1) We are going to study some basic properties of Toeplitz operators with positive measure symbols on the Fock-Sobolev Spaces of fractional order including boundedness, compactness and the Schatten p class. .2) We will characterize some basic properties of Toepliz operators with positive measure symbols on the Fock type spaces including boundedness, compactness and the Schatten p class..3) We will explore the basis of Hankel operators with bounded symbols on (vector-valued) Fock-Sobolev space of fractional order..3) We are to research the basic properties of the Haplitz operators and the product of two Hankel operators on the Weighted Fock Spaces with weight e^{-|z|^m}..Above are the basic problems in operator theory and operator algebra theory and they will have many applications in theory and more ignificance in the future.