一个含有理分式核的Hilbert积分不等式  

A Hilbert Integral Inequality Involving Rational Fraction Kernel

作　　者：有名辉[1] 孙洁[1] You Minghui;Sun Jie(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：《台州学院学报》2020年第6期19-23,共5页Journal of Taizhou University

摘　　要：通过引进参数,构造了一个分式型齐次核函数,并利用余切函数的有理分式展开,建立一个常数因子用余切函数表示的Hilbert型积分不等式,推广了经典的Hilbert积分不等式。另外,赋予结论中的参数不同的值,文中还给出了一些特殊情形。By introducing parameters,we construct a new homogeneous kernel function.According to the rational fraction expansion of cotangent function,a Hilbert-type integral inequality is established with the constant factor represented by the cotangent function.The new obtained result is proved to be an extension of the classical Hilbert’s inequality.In addition,specifying the parameters,some special case of known inequalities are presented.

关 键 词：HILBERT型不等式 HOLDER不等式 余切函数 有理分式展开 

分 类 号：O178[理学—数学]