超齐次核有界算子的构建条件及算子范数估计  

Construction Conditions for Bounded Operator with Super-Homogeneous Kernel and the Operator Norm

作　　者：洪勇 HONG Yong(Artificial Intelligence College,Guangzhou Huashang College,Guangzhou 511300,China;College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China)

机构地区：[1]广州华商学院人工智能学院,广州511300 [2]广东财经大学统计与数学学院,广州510320

出　　处：《数学年刊(A辑)》2024年第3期297-308,共12页Chinese Annals of Mathematics

基　　金：广州华商学院特色科研项目(No.2024HSTS08);广东省基础与应用基础研究基金(No.2022A1515012429)的资助.

摘　　要：引入超齐次函数的概念,利用权函数方法和实分析技巧.首先建立具有超齐次核的半离散Hilbert型不等式.然后利用所得结果讨论超齐次核积分算子和离散算子,得到加权Lebesgue空间和加权赋范序列空间之间有界算子的构造条件和算子范数估计。最后给出一些特例.By introducing the concept of super-homogeneous function,using the weight function method and real analysis techniques.Firstly,semi-discrete Hilbert-type inequality with super-homogeneous kernel is established.Then the integral and discrete operators with super-homogeneous kernel are discussed suing the results obtained,the construction conditions of bounded operators between weighed Lebesgue space and weighed normed sequence space and the operator norm are obtained.Finally some special cases are given.

关 键 词：超齐次核 有界积分算子 有界离散算子 半离散Hilbert型不等式 加权Lebesgue 空间 加权赋范序列空间 算子范数 

分 类 号：O177[理学—数学]