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中国科学院大学学报 ›› 2016, Vol. 33 ›› Issue (6): 729-735.DOI: 10.7523/j.issn.2095-6134.2016.06.002

• 数学与物理学 • 上一篇    下一篇

一个双参数Hilbert型积分算子及其应用

孙文兵, 刘琼   

  1. 邵阳学院理学与信息科学系, 湖南 邵阳 422000
  • 收稿日期:2016-03-18 发布日期:2016-11-15
  • 通讯作者: 刘琼,E-mail:liuqiongxx13@163.com
  • 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

SUN Wenbing, LIU Qiong   

  1. Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan, China
  • Received:2016-03-18 Published:2016-11-15
  • Supported by:

    Supported by the National Natural Science Foundation of China(11171280)

摘要:

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

Abstract:

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.

Key words: two-parameter Hilbert-type integral operator, norm, weight function, the best constant factor, Hilbert-type integral inequality

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