含混合核的Hilbert型不等式及应用  

A Hilbert-Type Inequality Involving a Mixed Kernel and Its Application

作　　者：有名辉[1] 王晓宇 YOU Minghui;WANG Xiaoyu(Mathematics Teaching and Research Office,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou,Zhejiang 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：《绍兴文理学院学报》2021年第10期47-53,共7页Journal of Shaoxing University

基　　金：浙江机电职业技术学院科教融合项目“关联平均算子的Hilbert型不等式的研究”(A-0271-20);浙江机电职业技术学院科教融合项目培育和孵化工程项目(A-0271-21-206).

摘　　要：通过引入多个参数,构建一个与对数函数和指数函数有关、并且同时包含齐次和非齐次两种形态的混合核函数.由此建立与新构建的核函数相关联的Hilbert型积分不等式,且常数因子是最佳的.通过对参数赋予特殊的数值,证明了新建立的不等式是已有一些结论的推广,并给出若干新的含有Catalan常数等特殊常数的Hilbert型不等式.By introducing several parameters,a mixed kernel function related to exponent and logarithmic functions and including both homogeneous and non-homogeneous forms was constructed.Then,the Hilbert type integral inequality associated with the new kernel was established,and the constant factor was proved to be the best possible.By assigning special values to the parameters,the newly obtained inequality proves to be an extension of some existing results.Furthermore,some new special Hilbert-type inequalities with the constant factors related to special constants such as Catalan constant are presented at the end of the paper.

关 键 词：HILBERT型不等式 GAMMA函数 混合核 麦克劳林展开 Catalan常数 

分 类 号：O174.1[理学—数学]