非齐次核最佳半离散Hilbert型逆向不等式的等价条件及算子表示  

Equivalent Conditions and Operator Expressions forthe Best Half-Discrete Hilbert-Type InverseInequality with Non-homogeneous Kernel

作　　者：洪勇 张丽娟 孔荫莹 李真 HONG Yong;ZHANG Lijuan;KONG Yinying;LI Zhen(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4期823-830,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);广东省教育科学规划项目(批准号:2021GXJK201).

摘　　要：首先,利用权函数方法讨论非齐次核K(n,x)=G(n^(λ1)x^(λ2))(λ_(1)λ_(2)>0)的半离散Hilbert型逆向不等式,给出最佳半离散Hilbert型逆向不等式的等价条件及各参数间的关系;其次,作为应用给出等价的算子表示及若干特例.Firstly,by using the power function method,we discussed the half-discrete Hilbert-type inverse inequality with non-homogeneous kernel K(n,x)=G(n^(λ1)x^(λ2))(λ_(1)λ_(2)>0),gave equivalent conditions for the best half-discrete Hilbert-type inverse inequality and the relationship between the parameters.Secondly,as an application,we gave the equivalent operator expressions and some special cases.

关 键 词：非齐次核 半离散Hilbert型逆向不等式 最佳常数因子 算子表示 BETA函数 

分 类 号：O178[理学—数学]