一个全平面上的Hilbert型不等式及应用  

A Hilbert Type Inequality on Whole Plane and Its Applications

作　　者：有名辉[1] YOU Minghui(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou,Zhejiang 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：《宜宾学院学报》2020年第12期59-63,共5页Journal of Yibin University

基　　金：浙江省教育厅一般科研资助项目(Y201737260)。

摘　　要：通过引入多个参变量,构建一个定义在全平面上的混合核函数,并建立与之关联的具有最佳常数因子的Hilbert型不等式.通过变量替换,将非齐次型核函数转化为齐次型,并得到相应的Hilbert型不等式.另外,通过对参量赋予特殊值,借助余切函数的部分分式展开,得到最佳常数因子与余切函数高阶导数关联的Hilbert型不等式.最后还给出其它一些特殊的结果.By introducing several parameter variables,a mixed kernel function defined on the whole plane was constructed,and the Hilbert-type inequality with the best constant factor associated with the constructed kernel was established.In addition,the non-homogeneous kernel function was transformed into homogeneous type through variable substitution,and the corresponding Hilbert-type inequality was obtained.Furthermore,giving special values to the parameters,and using the partial fraction expansion of the cotangent function,some special Hilbert-type inequality with the best constant factor related to the higher derivative of the cotangent function was obtained.Finally,some other special results are put forward.

关 键 词：HILBERT型不等式 混合核 Hölder不等式 余切函数 部分分式展开 

分 类 号：O174.1[理学—数学]