一个负齐次核的Hilbert型不等式及应用  

On a Hilbert-type integral inequality involving negative homogeneous kernel and its applications

作　　者：有名辉[1] YOU Ming-hui(Office of Mathematics Teaching and Research,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,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

出　　处：《高师理科学刊》2018年第3期1-6,共6页Journal of Science of Teachers＇College and University

基　　金：浙江省教育厅一般科研项目(Y201737260)

摘　　要：通过引进多个参数,借助实分析的技巧,建立了一个具有最佳常数因子并含有负齐次核的Hilbert型积分不等式,推广了相关文献的结果.作为结论的应用,给出了若干与某些特殊常数相关联的不等式.By introducing multi parameters,and using the method of real analysis,a Hilbert-type integral inequality involving the negative homogeneous kernel and the best possible constant factor is established,the result is extensions of the related literature′results.As applications of the obtained theorem,some new inequalities related to some special constants are presented.

关 键 词：HILBERT型不等式 EULER数 Catalan常数 BERNOULLI数 HOLDER不等式 GAMMA函数 

分 类 号：O178[理学—数学]