Hilbert型级数不等式的研究进展及应用

Abstract

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

CLC Number:

O178

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.

[1]	ZENG Zhihong, YANG Bicheng. A Half-Discrete Mulholland-Type Inequality Involving Multiple Variable Upper Limit Function and Partial Sums [J]. Journal of Jilin University Science Edition, 2026, 64(3): 511-0520.
[2]	ZHAO Qian, HONG Yong, KONG Yinying. Parameter Conditions of Optimal Hilbert-Type Integral Inequalities with Quasi-homogeneous Kernel in Weighted Lebesgue Spaces with Exponential Weight and Applications [J]. Journal of Jilin University Science Edition, 2024, 62(6): 1325-1333.
[3]	ZHANG Lijuan, HONG Yong, LIAO Jianquan. Inverse Problem for a Class of Bounded Integral Operators with Non-homogeneous Kernel [J]. Journal of Jilin University Science Edition, 2024, 62(4): 858-865.
[4]	WANG Aizhen, YANG Bicheng. A New Half-Discrete Hilbert-Type Inequality Involving Higher-Order Derivative Function and Partial Sums [J]. Journal of Jilin University Science Edition, 2023, 61(6): 1296-1304.
[5]	HONG Yong, ZHAO Qian. Construction Theorem of Semi-discrete Hilbert-Type Inverse Inequality with Generalized Homogeneous Kernel and Operator Representation#br# [J]. Journal of Jilin University Science Edition, 2023, 61(6): 1305-1312.
[6]	HONG Yong, ZHANG Lijuan, KONG Yinying, LI Zhen. Equivalent Conditions and Operator Expressions for the Best Half-Discrete Hilbert-Type Inverse Inequality with Non-homogeneous Kernel [J]. Journal of Jilin University Science Edition, 2023, 61(4): 823-830.
[7]	HONY Yong, CHEN Qiang. Optimal Matching Parameters for Inverse Hilbert-Type Integral Inequality with Non-homogeneous Kernel and Operator Expression#br# [J]. Journal of Jilin University Science Edition, 2022, 60(4): 845-852.
[8]	WANG Aizhen, YANG Bicheng. A New Half-Discrete Hilbert-Type Inequality Involving Higher-Order Derivative Function [J]. Journal of Jilin University Science Edition, 2022, 60(2): 240-246.
[9]	XIN Dongmei, YANG Bicheng, YAN Zhilai. Hardy-Hilbert-Type Integral Inequality with a Derivative Function [J]. Journal of Jilin University Science Edition, 2021, 59(6): 1380-1386.
[10]	HONG Yong, WU Chunyang, CHEN Qiang. Matching Parameter Conditions for the Best Hilbert-Type Integral Inequality with a Class of Non-homogeneous Kernels [J]. Journal of Jilin University Science Edition, 2021, 59(2): 207-212.
[11]	HONG Yong, ZENG Zhihong. Necessary and Sufficient Condition for Establishmentof HalfDiscrete HilbertType Inequality with Kernel G(n^λ1/x^λ2)(λ₁λ₂>0) and Its Application#br# [J]. Journal of Jilin University Science Edition, 2020, 58(3): 507-512.
[12]	XIN Dongmei, YANG Bicheng. A HalfDiscrete HilbertType Inequality of More Accurate Strengthened Version [J]. Journal of Jilin University Science Edition, 2020, 58(2): 225-230.
[13]	QIU Ke’e, CHEN Songliang, DENG Xicai, TAO Lei, LIU Zhuo. A Class of Inequalities of Hadamard with Local Fractional Integrals for Generalized s-Convex Functions on Fractal Sets and Their Applications#br# [J]. Journal of Jilin University Science Edition, 2019, 57(04): 793-802.
[14]	SUN Wenbing. Hadamard Type Fractional Integral Inequalities withParameter for Harmonically Quasiconvex Functions [J]. Journal of Jilin University Science Edition, 2019, 57(04): 803-808.
[15]	HONG Yong. Equivalent Condition for Obtaining the Best Constant Factorof HilbertType Multiple Series Inequalities with Homogeneous Kernel and Applications#br# [J]. Journal of Jilin University Science Edition, 2019, 57(2): 191-198.

Research Progress and Applications of Hilbert-Type Series Inequalities

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