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

HONG Yong, HE Bing

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

Chinese Quarterly Journal of Mathematics >

2021 , Vol. 36 >Issue 3: 252 - 262

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.03.004

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

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

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.

Received date: 2021-04-22

Online published: 2021-10-08

Supported by

Supported by National Natural Science Foundation of China (Grant No. 12071491);
Guangzhou Science and Technology Plan Project (Grant No. 202102080177).

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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

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

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