具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用

doi:10.13371/j.cnki.chin.q.j.m.2021.03.004

数学季刊 ›› 2021, Vol. 36 ›› Issue (3): 252-262.doi: 10.13371/j.cnki.chin.q.j.m.2021.03.004

具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用

1. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China;
2. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China.

收稿日期:2021-04-22 出版日期:2021-09-30 发布日期:2021-10-08
通讯作者: HE Bing (1980-), male, native of Xinyi, Guangdong, associate professor of Guangdong University of Education, engages in differential equations and analytical inequalities.
作者简介:HONG Yong (1959-), male, native of Zhaotong, Yunnan, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities; HE Bing (1980-), male, native of Xinyi, Guangdong, associate professor of Guangdong University of Education, engages in differential equations and analytical inequalities.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 12071491);
Guangzhou Science and Technology Plan Project (Grant No. 202102080177).

The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications

1. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China;
2. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China.

Received:2021-04-22 Online:2021-09-30 Published:2021-10-08
Contact: HE Bing (1980-), male, native of Xinyi, Guangdong, associate professor of Guangdong University of Education, engages in differential equations and analytical inequalities.
About author:HONG Yong (1959-), male, native of Zhaotong, Yunnan, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities; HE Bing (1980-), male, native of Xinyi, Guangdong, associate professor of Guangdong University of Education, engages in differential equations and analytical inequalities.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 12071491);
Guangzhou Science and Technology Plan Project (Grant No. 202102080177).

摘要/Abstract

摘要： By using the weight function method, the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K ( n,||x|| _ρ,m ) = G ( n^{λ 1} ||x|| ^{λ 2}_ρ,m) are discussed, some equivalent conditions of the optimal matching parameter are established, and the expression of the optimal constant factor is obtained. Finally, their applications in operator theory are considered.

关键词: Non-homogeneous kernel, Half discrete Hilbert type multiple integral inequality, Best constant factor, Optimal matching parameter, Operator norm, Bounded operator

Abstract: By using the weight function method, the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K ( n,||x|| _ρ,m ) = G ( n^{λ 1} ||x|| ^{λ 2}_ρ,m) are discussed, some equivalent conditions of the optimal matching parameter are established, and the expression of the optimal constant factor is obtained. Finally, their applications in operator theory are considered.

Key words: Non-homogeneous kernel, Half discrete Hilbert type multiple integral inequality, Best constant factor, Optimal matching parameter, Operator norm, Bounded operator

中图分类号:

O178

洪勇, 和炳.

具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用 [J]. 数学季刊, 2021, 36(3): 252-262.

HONG Yong, HE Bing . The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(3): 252-262.

具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用

The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications

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