多参数复合核的Hilbert型不等式及应用  

On a Hilbert-type Inequality Involving a Composite Kernel with Several Parameters and Its Applications

作　　者：有名辉[1] 董飞 何振华 YOU Ming-hui;DONG Fei;HE Zhen-hua(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

出　　处：《通化师范学院学报》2020年第12期23-27,共5页Journal of Tonghua Normal University

基　　金：浙江省教育厅科研项目(Y201737260);浙江机电职业技术学院科教融合项目(A-0271-20-007);广西财经学院博士基金项目(BS2019026)。

摘　　要：引入若干参数,构造一个与指数函数和对数函数相关、并且同时包含齐次和非齐次两种情形的复合型核函数.借助分析的有关技巧,建立了一个新的Hilbert型积分不等式,并证明了常数因子是最佳的.作为定理的应用,对参数赋予特殊数值,最后给出了一些特殊结果.In this work,by introducing some parameters,a composite kernel function which is related to exponential function and logarithmic function,and contains both homogeneous and non-homogeneous cases is constructed.By means of some techniques of real analysis,a new Hilbert type integral inequality is established,and it is proved that the constant factor is optimal.In particular,as an application of the theorem,special values are given to the parameters,and some special results are established at the end of the paper.

关 键 词：HILBERT型不等式 复合核函数 麦克劳林级数 最佳因子 

分 类 号：O178[理学—数学]