具有齐次核的Hilbert型积分不等式的构造特征及应用

Journal of Jilin University Science Edition

Structural Characteristics and Applications of Hilbert’s TypeIntegral Inequalities with Homogenous Kernel

HONG Yong

College of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China

Received:2016-10-19 Online:2017-03-26 Published:2017-03-24
Contact: HONG Yong E-mail:hongyonggdcc@yeah.net

Abstract

Abstract: By using the technique of real analysis, the author studied the structural characteristics of Hilbert’[KG-*5]s type integral inequalities with homogeneous kernel and the necessary and sufficient condition for obtaining the best constant factor, and obtained the analytical expression of the best constant factor.

Key words: the best constant factor, necessary and sufficient condition, structural characteristics, Hilbert’s type integral inequality

CLC Number:

O178

HONG Yong. Structural Characteristics and Applications of Hilbert’s TypeIntegral Inequalities with Homogenous Kernel[J].Journal of Jilin University Science Edition, 2017, 55(02): 189-194.

[1]	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.
[2]	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.
[3]	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.
[4]	HONG Yong, ZENG Zhihong. Necessary and Sufficient Condition for Establishment ofHilbertType Series Inequality with a Class ofQuasihomogeneous Kernels and Its Application [J]. Journal of Jilin University Science Edition, 2018, 56(3): 530-536.
[5]	HONG Yong, WEN Yamin. Necessary and Sufficient Condition for a Class of HilbertType IntegralInequality with a Nonhomogeneous Kernel and Its Application [J]. Journal of Jilin University Science Edition, 2018, 56(2): 227-232.
[6]	LIU Qiong. A Multi-parameters HilbertType IntegralInequality Related to Extended Zeta Function [J]. Journal of Jilin University Science Edition, 2016, 54(06): 1294-1299.
[7]	HONG Yong. Multiple HilbertType Integral Inequalities withHomogeneous Kernel and Some Functions [J]. Journal of Jilin University Science Edition, 2016, 54(03): 408-401.
[8]	HONG Yong. A New Hilbert’s Type Integral Inequality with a Quasihomogeneous Kernel [J]. Journal of Jilin University Science Edition, 2015, 53(02): 177-182.
[9]	HONG Yong. A New Hilbert’s Type Integral Inequality withKernel of Transferable Variable Function [J]. Journal of Jilin University Science Edition, 2014, 52(01): 7-11.
[10]	LIU Qiong. A Hilberttype Integral Inequality with Several Parameters [J]. J4, 2009, 47(05): 903-908.
[11]	HONG Yong. A Hilbert’s Type Series Inequality and Its Application [J]. J4, 2008, 46(02): 189-192.
[12]	HONG Yong, XIANG Zigui. On a New Multiple Hilbert’s Integral Inequality with the Best Constant Factor [J]. J4, 2007, 45(02): 197-202.
[13]	LI Qing-chun,ZHAGN Shu-gong. Generalization and Application on Diagonal Dominance of Matrices [J]. J4, 2005, 43(05): 561-566.

Structural Characteristics and Applications of Hilbert’s TypeIntegral Inequalities with Homogenous Kernel

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