联系一些特殊函数的Hilbert型积分不等式及其算子范数表达式  

Hilbert-Type Integral Inequality Related to Some Special Functions and Its Operator Expressions with Norm

作　　者：刘琼 LIU Qiong(College of Science,Shaoyang University,Shaoyang 422000,Hunan Province,China)

机构地区：[1]邵阳学院理学院,湖南邵阳422000

出　　处：《吉林大学学报（理学版）》2018年第6期1359-1365,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11171280);湖南省教育厅教学改革项目(批准号:湘教通[2014]247号)

摘　　要：利用权函数方法、实分析技巧和特殊函数的相关理论,建立一个多参数的联系一些特殊函数的Hilbert型积分不等式及其等价式,证明其常数因子是最佳的,并给出其算子范数的表达式.By using the weight function method,the technique of the real analysis and the related theories of special functions,the author established a Hilbert-type integral inequality with multi-parameters related to some special functions and its equivalence,proved that its constant factors were optimal,and gave the operator expressions with the norm.

关 键 词：HILBERT型积分不等式 权函数 Whittaker函数 Hilbert型积分算子 合流超几何函数 

分 类 号：O178[理学—数学]