吉林大学学报(理学版) ›› 2023, Vol. 61 ›› Issue (4): 823-830.

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非齐次核最佳半离散Hilbert型逆向不等式的等价条件及算子表示

洪勇1, 张丽娟1, 孔荫莹2, 李真2   

  1. 1. 广州华商学院 应用数学系, 广州 511300; 2. 广东财经大学 统计与数学学院, 广州 510320
  • 收稿日期:2022-09-26 出版日期:2023-07-26 发布日期:2023-07-26
  • 通讯作者: 洪勇 E-mail:hongyonggdcc@yeah.net

Equivalent Conditions and Operator Expressions for the Best Half-Discrete Hilbert-Type Inverse Inequality with Non-homogeneous Kernel

HONG Yong1, ZHANG Lijuan1, KONG Yinying2, LI Zhen2   

  1. 1. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China;
    2. College of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
  • Received:2022-09-26 Online:2023-07-26 Published:2023-07-26

摘要:

首先, 利用权函数方法讨论非齐次核K(n,x)=G(nλ1xλ2)(λ1λ2>0)的半离散Hilbert型逆向不等式, 给出最佳半离散Hilbert型逆向不等式的等价条件及各参数间的关系; 其次, 作为应用给出等价的算子表示及若干特例.

关键词: 非齐次核, 半离散Hilbert型逆向不等式, 最佳常数因子, 算子表示, Beta函数

Abstract: Firstly, by using the power function method, we discussed the half-discrete Hilbert-type inverse inequality with non-homogeneous kernel K(n,x)=G(nλ1xλ2)(λ1λ2>0), gave equivalent conditions for the best half-discrete Hilbert-type inverse inequality and the relationship  between the parameters. Secondly,  as an application, we gave  the equivalent operator expressions and some special cases.

Key words: non-homogeneous kernel, half-discrete Hilbert-type inverse inequality, the best constant factor, operator expression, Beta function

中图分类号: 

  • O178