收稿日期: 2016-03-18
网络出版日期: 2016-11-15
基金资助
Supported by the National Natural Science Foundation of China(11171280)
On a two-parameter Hilbert-type integral operator and its applications
Received date: 2016-03-18
Online published: 2016-11-15
Supported by
Supported by the National Natural Science Foundation of China(11171280)
引入两个参数λ1和λ2，利用权函数方法和泛函分析技巧，定义一个双参数Hilbert型积分算子，并给出算子的范数.作为应用，获得一些改进的结果，并得到一些具有特殊核的新的Hilbert型积分不等式.
关键词： 双参数的Hilbert型积分算子; 范数; 权函数; 最佳常数因子; Hilbert型积分不等式
孙文兵 , 刘琼 . 一个双参数Hilbert型积分算子及其应用[J]. 中国科学院大学学报, 2016 , 33(6) : 729 -735 . DOI: 10.7523/j.issn.2095-6134.2016.06.002
In this work, by introducing two parameters λ1 and λ2 and using the method of weight function and the technique of functional analysis, a two-parameter Hilbert-type integral operator is defined and the norm of the operator is given. As applications, a few improved results and some new Hilbert-type integral inequalities with the particular kernels are obtained.
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