一个关联对数函数的Hilbert型不等式  

On a Hilbert-type inequality related to logarithmic function

作　　者：有名辉[1] 范献胜 何振华 YOU Minghui;FAN Xiansheng;HE Zhenhua(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou,Zhejiang 310053,China;School of Information and Statistics,Guangxi University of Finance and Economics,Nanning,Guangxi 530003,China)

机构地区：[1]浙江机电职业技术学院数学教研室,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：《贵州师范大学学报（自然科学版）》2022年第1期80-84,共5页Journal of Guizhou Normal University：Natural Sciences

基　　金：浙江省教育厅科研资助项目(Y2021737260);浙江机电职业技术学院科教融合项目(A-0271-21-206);广西财经学院博士基金项目(BS2019026)。

摘　　要：通过引入多个参变量,构造一个与对数函数有关,并且同时包含齐次核和非齐次核两种形态的积分核函数。利用经典分析的一些技巧,建立一个最佳常数因子用余切函数表示的Hilbert型不等式。特别地,对参数赋予特殊值,最后还给出了若干推论。By introducing several parameters, an integral kernel function related to logarithmic function and containing both homogeneous kernel and non-homogeneous kernel is constructed. By using some skills of classical analysis, a Hilbert-type inequality with the best constant factor expressed by cotangent function is established. In particular, the parameters are given special values, and some corollaries are presented at the end of the paper.

关 键 词：HILBERT型不等式 对数函数 ■不等式 勒贝格控制收敛定理 最佳因子 

分 类 号：O178[理学—数学]