一个含离散型分式核的Hilbert型不等式  

A Hilbert-type inequality with a discrete fractional kernel

作　　者：有名辉[1] 董飞 杨必成[2] YOU Ming-hui;DONG Fei;YANG Bi-cheng(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China;School of Mathematics,Guangdong University of Education,Guangzhou 510303,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]广东第二师范学院数学学院,广东广州510303

出　　处：《兰州理工大学学报》2024年第3期151-155,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(61772140);浙江省教育厅科研资助项目(Y202148139)。

摘　　要：引入若干正参数,新构建了一个分式型的离散形态的核函数,并借助于权系数的方法,建立了一个二重Hilbert型级数不等式,并证明此不等式的常数因子是最佳取值.另外,根据余割函数的有理分式展开形式,给出最佳常数因子的余割函数表示形式.通过对参数赋予一些特殊数值,得到了一些已有结果,并且给出了一些新的含特殊核函数的Hilbert型不等式.By introducing several positive parameters,a new fractional discrete kernel function is constructed.By means of the method of weight coefficients,a double Hilbert series inequality is established,and the constant factor of the newly obtained inequality is proved to be the best possible.Furthermore,based on the rational fraction expansion of the cosecant function,it is also proved that the optimal constant factor can be represented by the cosecant function.At last,by assigning some specific values to the parameters,some previously known results are obtained,and some new Hilbert-type inequalities with special kernel functions are also presented at the end of the paper.

关 键 词：HILBERT型不等式 分式型核函数 有理分式展开 余割函数 

分 类 号：O178[理学—数学]