Fock空间及其相关算子  

Fock spaces and relative operators

作　　者：胡璋剑[1] 吕小芬[1] 

机构地区：[1]湖州师范学院数学系,湖州313000

出　　处：《中国科学：数学》2015年第11期1759-1778,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11271124;11171277和11426104);浙江省自然科学基金(批准号:LY15A010014和LQ13A010005)资助项目

摘　　要：本文是关于Fock空间及其上相关算子研究的综述,包括Fock空间的定义、Fock空间的Bergman核估计和Carleson测度及其范数等价刻画等基本内容,并且展示了对Fock空间上相关线性算子(如复合算子、广义Ces`aro算子、Toeplitz算子和Hankel算子及某些线性算子所生成的闭代数)若干特性研究的最新进展,这些特性包括有界性、紧性、Schatten类和Schatten-Herz类等.This paper is a timely survey on generalized Fock spaces and operators acting on them. It contains the definition of Fock spaces with various weights, the precise estimates on the Bergman kernel, the equivalent norms and the Carleson measures. Also, some recent progress on the study of certain operators on Fock spaces is introduced, which includes composition operators, extended Cesaro operators, Toeplitz operators, Hankel operators, and those in the closed algebra generated by weakly localized operators.

关 键 词：FOCK空间 BERGMAN核 CARLESON测度 TOEPLITZ算子 HANKEL算子 

分 类 号：O177[理学—数学]