一个含离散型分式核的Hilbert型不等式

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (3): 151-155.

一个含离散型分式核的Hilbert型不等式

有名辉¹, 董飞¹, 杨必成^*2

1.浙江机电职业技术学院数学教研室, 浙江杭州 310053;
2.广东第二师范学院数学学院, 广东广州 510303

收稿日期:2022-11-25 出版日期:2024-06-28 发布日期:2024-07-02
通讯作者: 杨必成(1946-),男,广东汕尾人,教授.Email:bcyang@gdei.edu.cn
基金资助:
国家自然科学基金(61772140),浙江省教育厅科研资助项目(Y202148139)

A Hilbert-type inequality with a discrete fractional kernel

YOU Ming-hui¹, DONG Fei¹, YANG Bi-cheng²

1. Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China;
2. School of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Received:2022-11-25 Online:2024-06-28 Published:2024-07-02

摘要/Abstract

摘要： 引入若干正参数,新构建了一个分式型的离散形态的核函数,并借助于权系数的方法,建立了一个二重Hilbert型级数不等式,并证明此不等式的常数因子是最佳取值.另外,根据余割函数的有理分式展开形式,给出最佳常数因子的余割函数表示形式.通过对参数赋予一些特殊数值,得到了一些已有结果,并且给出了一些新的含特殊核函数的Hilbert型不等式.

关键词: Hilbert型不等式, 分式型核函数, 有理分式展开, 余割函数

Abstract: By introducing several positive parameters, a new fractional discrete kernel function is constructed. By means of the method of weight coefficients, a double Hilbert series inequality is established, and the constant factor of the newly obtained inequality is proved to be the best possible. Furthermore, based on the rational fraction expansion of the cosecant function, it is also proved that the optimal constant factor can be represented by the cosecant function. At last, by assigning some specific values to the parameters, some previously known results are obtained, and some new Hilbert-type inequalities with special kernel functions are also presented at the end of the paper.

Key words: Hilbert-type inequality, fractional kernel function, rational fraction expansion, cosecant function

中图分类号:

O178

有名辉, 董飞, 杨必成. 一个含离散型分式核的Hilbert型不等式[J]. 兰州理工大学学报, 2024, 50(3): 151-155.

YOU Ming-hui, DONG Fei, YANG Bi-cheng. A Hilbert-type inequality with a discrete fractional kernel[J]. Journal of Lanzhou University of Technology, 2024, 50(3): 151-155.

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