一类推广的Hilbert型不等式  

A Class of Generalized Hilbert-Type Inequalities

作　　者：有名辉[1] 王晓宇 何振华 YOU Minghui;WANG Xiaoyu;HE Zhenhua(Basic Teaching Department,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China;School of Information and Statistics,Guangxi University of Finance and Economics,Nanning 530003,China)

机构地区：[1]浙江机电职业技术学院公共基础教学部,浙江杭州310053 [2]广西财经学院信息与统计学院,广西南宁530003

出　　处：《安庆师范大学学报（自然科学版）》2021年第4期80-84,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：浙江省教育厅科研资助项目(Y201737260);广西财经学院博士基金项目(BS2019026);浙江机电职业技术学院科教融合项目(A-0271-21-206)。

摘　　要：Hilbert型不等式是解析不等式的重要组成部分,在分析学以及相关领域有着极为重要的作用。通过引入若干参数,构造了一个一般形态的分式型核函数,并利用权系数的方法和实分析的技巧,建立了含有最佳常数因子的Hilbert型不等式,推广了相关文献的结果。此外,借助余切函数的部分分式展开公式,给出了所构建不等式的最佳常数因子的三角函数表示形式。Hilbert-type inequality is an important part of analytic inequality,and plays a very important role in analysis and related fields.By introducing some parameters,a fractional kernel function in general form is constructed.Using the method of weight coefficient and the technique of real analysis,a Hilbert-type inequality with the best constant factor is established,which generalizes the results of relevant literature.In addition,with the help of the partial fraction expansion formula of the cotangent function,the trigonometric function representation of the best constant factor in the newly obtained inequality is given.

关 键 词：HILBERT型不等式 余切函数 部分分式展开 H?lder不等式 最佳因子 

分 类 号：O178[理学—数学]