一类具有非齐次核的Hilbert型积分不等式成立的充要条件及其应用

Journal of Jilin University Science Edition

Previous Articles Next Articles

Necessary and Sufficient Condition for a Class of HilbertType IntegralInequality with a Nonhomogeneous Kernel and Its Application

HONG Yong, WEN Yamin

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

Received:2017-08-09 Online:2018-03-26 Published:2018-03-27
Contact: HONG Yong E-mail:hongyonggdcc@yeah.net

Abstract

Abstract: By means of methods and techniques of real analysis, we discussed the necessary and sufficient condition and the best constant factor for a class of Hilberttype integral inequality with a nonhomoeneous kernel K(x,y)=G(x^λ₁y^λ₂), and studied its application in the operator theory.

Key words: nonhomoeneous kernel, the best constant factor, norm of operator, bounded linear operator, Hilberttype integral inequality, necessary and sufficient condition

CLC Number:

O178

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.

[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]	LIU Qiong. HilbertType Integral Inequality Related to Some SpecialFunctions and Its Operator Expressions with Norm#br# [J]. Journal of Jilin University Science Edition, 2018, 56(6): 1359-1365.
[5]	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.
[6]	YANG Bicheng, CHEN Qiang. Equivalent Conditions of Existence of a Class of Reverse HardyType Integral Inequalities with Nonhomogeneous Kernel [J]. Journal of Jilin University Science Edition, 2017, 55(04): 804-808.
[7]	GU Zhaohui, YANG Bicheng. A HilbertType Integral Inequality in Whole PlaneRelated to Gamma Function of Best Constant Factor [J]. Journal of Jilin University Science Edition, 2017, 55(03): 513-518.
[8]	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.
[9]	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.
[10]	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.
[11]	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.
[12]	YANG Bicheng, CHEN Qiang. A HilbertType Integral Inequality Related to the Riemann Zeta Function [J]. Journal of Jilin University Science Edition, 2014, 52(05): 869-872.
[13]	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.
[14]	XIE Zitian, ZENG Zheng, ZHOU Qinghua. A New Hilbert-Type Integral Inequality-with-the Homogeneous [J]. J4, 2012, 50(4): 693-697.
[15]	YANG Bi-Cheng. A Reverse HilbertType Integral Inequality with a Nonhomogeneous Kernel [J]. J4, 2011, 49(03): 437-441.

Necessary and Sufficient Condition for a Class of HilbertType IntegralInequality with a Nonhomogeneous Kernel and Its Application

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10