一个R^2上含双曲函数核的Hilbert型不等式  

A Hilbert-type inequality defined on R^2 with the kernel involving hyperbolic functions

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 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：《浙江大学学报（理学版）》2020年第5期554-558,共5页Journal of Zhejiang University（Science Edition）

基　　金：浙江机电职业技术学院科教融合一般项目(A-0271-20-007).

摘　　要：通过引入参数,构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开,建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。作为应用,通过赋予参数不同的值,建立了一些有意义的特殊结果。By introducing some parameters,we construct a non-homogeneous kernel function including hyperbolic functions on the whole plane.In addition,by using the rational fraction expansion of tangent function,a Hilbert-type integral inequality associated with the best possible constant factor and the higher derivatives of tangent function is presented.Furthermore,some meaningful and special results are presented by specializing the parameters with different values as on application.

关 键 词：HILBERT型不等式 正切函数 双曲函数 有理分式展开 GAMMA函数 

分 类 号：O178[理学—数学]