拟齐次核的Hilbert型级数不等式的最佳搭配参数条件及应用

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 26-34.

拟齐次核的Hilbert型级数不等式的最佳搭配参数条件及应用

洪勇¹(),陈强²()

¹ 广州华商学院应用数学系广州 511300
² 广东第二师范学院计算机学院广州 510303

收稿日期:2020-10-28 出版日期:2022-02-01 发布日期:2022-02-23
作者简介:洪勇, E-mail: hongyonggdcc@yeah.net|陈强, E-mail: cq_c120m3@163.com
基金资助:
国家自然科学基金(61772140)

The Best Matching Parameters Conditions of Hilbert-Type Series Inequality with Quasi-Homogeneous Kernel and Applications

Yong Hong¹(),Qiang Chen²()

¹ Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300
² School of Computer, Guangdong University of Education, Guangzhou 510303

Received:2020-10-28 Online:2022-02-01 Published:2022-02-23
Supported by:
the NSFC(61772140)

摘要/Abstract

摘要：

选择搭配参数$ a，b$，利用权函数方法可得Hilbert型级数不等式 $ \sum\limits_{n=1}^{\infty}\sum\limits_{m=1}^{\infty}K(m, n)a_{m}b_{n}\leq M(a, b)\|\tilde{a}\|_{p, \alpha(a, b)}\|\tilde{b}\|_{q, \beta(a, b)}. $ 该文讨论$ a，b$应如何选取才能使具有拟齐次核的不等式中$ M（a，b）$为最佳常数因子的问题，得到了$a，b $为最佳搭配参数的充分必要条件及最佳常数因子的表达式.最后讨论其在求算子范数中的应用.

关键词: Hilbert型级数不等式, 拟齐次核, 最佳常数因子, 最佳搭配参数, 算子范数

Abstract:

Choosing $ a, b$ as the matching parameters, we can sue the weight function method to obtain Hilbert-type series inequality $\sum\limits_{m=1}^{\infty}\sum\limits_{n=1}^{\infty}K(m, n)a_{m}b_{n}\leq M(a, b)\|\tilde{a}\|_{p, \alpha(a, b)}\|\tilde{b}\|_{q, \beta(a, b)}.$ in the paper, the problem of how to choose $a, b $ in order to make $ M(a, b)$ the best constant factor in inequality with quasi-homogeneous kernels are discussed, necessary and sufficient conditions are obtained for $a, b $ to the best matching parameters, the formula for the best constant factor is obtained. Finally, their applications to solving operator morn are discussed.

Key words: Hilbert-type series inequality, Quasi-homogeneous kernel, The best constant factor, The best matching parameter, Operator norm

中图分类号:

O178

洪勇,陈强. 拟齐次核的Hilbert型级数不等式的最佳搭配参数条件及应用[J]. 数学物理学报, 2022, 42(1): 26-34.

Yong Hong,Qiang Chen. The Best Matching Parameters Conditions of Hilbert-Type Series Inequality with Quasi-Homogeneous Kernel and Applications[J]. Acta mathematica scientia,Series A, 2022, 42(1): 26-34.

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