构建超齐次核有界离散算子的参数条件及算子范数估计  

Parameter Conditions for Constructing Bounded Discrete Operators with Super-Homogeneous Kernel and Estimation of the Operator Norm

作　　者：洪勇 赵茜 Hong Yong;Zhao Qian(College of Data Science,Guangzhou Huashang College,Guangzhou 511300)

机构地区：[1]广州华商学院数据科学学院,广州511300

出　　处：《数学物理学报（A辑）》2024年第4期837-846,共10页Acta Mathematica Scientia

基　　金：广东省基础与应用基础研究基金(2022A1515012429);广州华商学院科研团队项目(2021HSKT03)。

摘　　要：引入超齐次函数的概念,首先构建超齐次核的Hilbert型离散不等式,然后利用Hilbert型不等式与同核算子的关系,讨论超齐次核离散算子,得到加权赋范序列空间中超齐次核有界离散算子的构建条件,解决了算子是否有界的判定方法和算子范数的估计问题.Introducing the concept of super-homogeneous function,firstly constructing the Hilbert-type discrete inequality with super-homogeneous kernel,and then discussing discrete operator with super-homogeneous kernel by using the relationship between Hilbert-type inequality and operator with the same kernel,obtained the construction conditions for bounded discrete operators with super-homogeneous kernel in weighted normed sequence spaces,and a method for determining whether an operator is bounded or not and the estimation of operator norm are solved.

关 键 词：超齐次核 有界算子 加权序列空间 有界算子的判定 Hilbert型离散不等式 算子范数 

分 类 号：O177[理学—数学]