一个新的多参数非齐次核Hilbert型积分不等式  

A New Hilbert-type Integral Inequality with Multi-parameter Nonhomogeneous Kernel

作　　者：刘琼 LIU Qiong(School of Science,Shaoyang University,Shaoyang 422000,China)

机构地区：[1]邵阳学院理学院,湖南邵阳422000

出　　处：《邵阳学院学报（自然科学版）》2018年第6期1-7,共7页Journal of Shaoyang University：Natural Science Edition

基　　金：国家自然科学基金项目资助(11171280);湖南省教育厅科学研究资助项目(10C1186)

摘　　要：文中引入多个参数,利用权函数方法、实分析技巧和拉普拉斯积分变换,建立一个新的多参数非齐次核Hilbert型积分不等式,同时考虑了它的等价式,证明了它们的常数因子是最佳的。在应用中通过选取一些特殊参数值,得到了一些有意义的结果。By introducing some parameters,and using the way of weight function and the technic of real analysis and Laplace s integral transform,a new Hilbert-type integral inequality with the inhomogeneous kernel and multi-parameters was given.Considering its equivalence,it was proved that their constant factors were optimal.As an application,some meaningful results were obtained by selecting some special parameters.

关 键 词：HILBERT型积分不等式 权函数 最佳常数因子 拉普拉斯积分变换 

分 类 号：O178[理学—数学]