一个混合核Hilbert型积分不等式及其算子范数表达式

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 369-378.

一个混合核Hilbert型积分不等式及其算子范数表达式

刘琼¹(),刘英迪²

¹ 邵阳学院理学院湖南邵阳 422000
² 邵阳学院经济管理学院湖南邵阳 422000

收稿日期:2018-10-26 出版日期:2020-04-26 发布日期:2020-05-21
作者简介:刘琼, E-mail:liuqiongxx13@163.com
基金资助:
湖南教育厅科学研究项目(19A455);湖南教育厅科学研究项目(18B433);湖南省教育厅教学改革项目(湘教通[2014]247号，No：448)

A Hilbert-Type Integral Inequality with the Mixed Kernel and Its Operator Expressions with Norm

Qiong Liu¹(),Yindi Liu²

¹ College of Science, Shao Yang University, Hunan Shaoyang 422000
² College of Economics and Management, Shaoyang University, Hunan Shaoyang 422000

Received:2018-10-26 Online:2020-04-26 Published:2020-05-21
Supported by:
the Scientific Research Project of Hunan Education Department(19A455);the Scientific Research Project of Hunan Education Department(18B433);the Teaching Reform Project of Hunan Education Department(湘教通[2014]247号，No：448)

摘要/Abstract

摘要：

利用权函数方法、实分析技巧和特殊函数理论，建立了一个联系Whittaker函数的混合核Hilbert型积分不等式及其等价式，证明了它们的常数因子是最佳的.并给出其算子范数表达式.

关键词: Hilbert型积分不等式, 权函数, Whittaker函数, 混合核, 算子表达式

Abstract:

By using the method of weight function, the technique of real analysis and the theory of special functions, a Hilbert-type integral inequality with the mixed kernel and its equivalent form are established, the optimality for the constant factors are proved and the operator expressions with norm are given.

Key words: Hilbert-type integral inequality, Weight function, Whittaker function, Mixed kernel, Operator expression

中图分类号:

O178

刘琼,刘英迪. 一个混合核Hilbert型积分不等式及其算子范数表达式[J]. 数学物理学报, 2020, 40(2): 369-378.

Qiong Liu,Yindi Liu. A Hilbert-Type Integral Inequality with the Mixed Kernel and Its Operator Expressions with Norm[J]. Acta mathematica scientia,Series A, 2020, 40(2): 369-378.

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