一个含有复合核的Hilbert型不等式  

On a Hilbert-type Inequality Involving a Composite Kernel

作　　者：有名辉[1] 孙霞[1] YOU Minghui;SUN Xia(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou,China 310053)

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

出　　处：《温州大学学报（自然科学版）》2021年第4期12-17,共6页Journal of Wenzhou University(Natural Science Edition)

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)。

摘　　要：通过引入恰当参数,构建一个与对数函数相关联并同时包含齐次和非齐次两种情形的核函数.借助实分析的相关技巧,建立一个含最佳常数因子的Hilbert型积分不等式.特别地,作为结论的应用,通过对参数赋予特殊值,文末还建立了若干推论.By introducing several parameters,this paper constructs a composite kernel function which is associated with logarithmic function and contains both homogeneous and non-homogeneous cases.With the help of real analysis techniques,a Hilbert-type integral inequality with optimal constant factor is established.In particular,as an application of the conclusion,some inferences are established by assigning special values to parameters.

关 键 词：HILBERT型不等式 复合核 Hölder不等式 最佳因子 

分 类 号：O178[理学—数学]