广义齐次核半离散Hilbert型逆向不等式的构造定理及算子表示  

Construction Theorem of Semi-discrete Hilbert-Type Inverse Inequality with Generalized Homogeneous Kernel and Operator Representation

作　　者：洪勇 赵茜 HONG Yong;ZHAO Qian(Department of Applied Mathematics,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]广州华商学院应用数学系,广州511300 [2]广东财经大学统计与数学学院,广州510320

出　　处：《吉林大学学报（理学版）》2023年第6期1305-1312,共8页Journal of Jilin University:Science Edition

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

摘　　要：利用权系数方法和实分析技巧,讨论具有广义齐次核的半离散Hilbert型逆向不等式的构造问题,给出构造这类不等式的充分必要条件和最佳常数因子的计算公式以及不等式的算子表示.Using the weight coefficient method and real analysis techniques,we discussed the problems of constructing semi-discrete Hilbert-type inverse inequality with generalized homogeneous kernel,gave necessary and sufficient conditions for constructing such inequality,the calculating formula of the best constant factor,and the operator expression of the inequality.

关 键 词：半离散Hilbert型逆向不等式 广义齐次核 构造定理 充要条件 最佳常数因子 积分算子 离散算子 

分 类 号：O178[理学—数学]