Hilbert型级数不等式的研究进展及应用

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (5): 1131-1140.

Hilbert型级数不等式的研究进展及应用

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科学系, 广州 510303

收稿日期:2021-04-21 出版日期:2021-09-26 发布日期:2021-09-26
通讯作者: 洪勇 E-mail:hongyonggdcc@yeah.net

Research Progress and Applications of Hilbert-Type Series Inequalities

HONG Yong¹, CHEN Qiang²

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

Received:2021-04-21 Online:2021-09-26 Published:2021-09-26

摘要/Abstract

摘要： 通过对Hilbert型级数不等式各阶段研究特点的分析, 对Hilbert型级数不等式由浅入深、由特殊到一般、由齐次核到非齐次核以及由低维到高维的发展历程和研究现状进行分析综述, 并给出部分最新研究成果.

关键词: Hilbert型级数不等式, 研究进展, 研究现状, 理论体系, 权函数方法, 级数算子

Abstract: Through the analysis of the research characteristics of Hilbert-type series inequalities in each stage, we analyzed and summarized
the development process and the current status of research of Hilbert-type series inequalities from simple to deep, from special to general, from homogeneous kernel to non-homogeneous kernel and from low dimension to high dimension, and gave some of the latest research results.

Key words: Hilbert-type series inequality, research progress, current status of research, theoretical system, weigh function method, series operator

中图分类号:

O178

洪勇, 陈强. Hilbert型级数不等式的研究进展及应用[J]. 吉林大学学报(理学版), 2021, 59(5): 1131-1140.

HONG Yong, CHEN Qiang. Research Progress and Applications of Hilbert-Type Series Inequalities [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1131-1140.

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