三圆盘Hardy空间上的Toeplitz算子与小Hankel算子的交换性  

Commutativity of Toeplitz Operator and Small Hankel Operator on Three-disk Hardy Spaces

作　　者：钟意 许安见 ZHONG Yi;XU Anjian(College of Science,Chongqing University of Technology,Chongqing 401320,China)

机构地区：[1]重庆理工大学理学院,重庆401320

出　　处：《兰州工业学院学报》2024年第2期91-96,共6页Journal of Lanzhou Institute of Technology

基　　金：国家自然科学基金面上项目(11871127);重庆市教委科学技术研究项目(KJZD-K202301109)。

摘　　要：Toeplitz算子的交换性问题是算子理论中的一个研究热点,在不同的函数空间下有不同的体现。在H^(2)(D^(3))空间上,对等式T^(*)_(f)H_(g)=H_(g)T_(f*)进行了研究,给出了f与g为一般函数和特殊函数时,T^(*)_(f)H_(g)=H_(g)T_(f*)成立的充要条件,再针对Toeplitz算子与小Hankel算子在三圆盘上的交换性问题,利用函数的多重Fourier分解,取三圆盘的一组正规正交基,通过算子作用在正规正交基上,得到Toeplitz算子与小Hankel算子可交换的充要条件。在H^(2)(D^(n))上也有类似的结论成立。The commutativity problem of Toeplitz operator is a hot topic in operator theory,which has different manifestations in different function spaces.In this paper,the equation T^(*)_(f)H_(g)=H_(g)T_(f*) is studied on the Hardy space of three disks,and the sufficient and necessary conditions are given when f and g are general functions and special functions.Then,aiming at the commutativity problem of Toeplitz operator and small Hankel operator on three disks,a set of normal orthogonal basis of three disks is taken by using multiple Fourier decomposition of the function.The necessary and sufficient conditions for commutative Toeplitz operator and small Hankel operator are obtained by operating operators on normal orthogonal basis.A similar conclusion holds for n-disk Hardy Spaces.

关 键 词：TOEPLITZ算子 小Hankel算子 HARDY空间 

分 类 号：O177.1[理学—数学]