一类非齐次核的最佳Hilbert型积分不等式的搭配参数条件

Abstract

Abstract: Firstly, by using the weight function method, we considered how to determine the matching parameters so that the Hilbert-type integral inequalities with non-homogeneous kernel G(x^λ₁y^λ₂)(λ₁λ₂>0) had the best constant factor. Secondly, we gave the necessary and sufficient conditions for the best matching parameter and the discriminant for fast determination of the best constant factor. Finally, we discussed applications of the best matching parameter in the integral operator theory.

Key words: non-homogeneous kernel, Hilbert-type integral inequality, the best constant factor, the best matching parameter, discriminant, operator norm, bounded operator

CLC Number:

O178

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.

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[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.
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[13]	HONG Yong. Norm of a Hilbert Singular Multiple Integral Operator with Parameters [J]. J4, 2011, 49(01): 21-26.
[14]	LIU Qiong. A Hilberttype Integral Inequality with Several Parameters [J]. J4, 2009, 47(05): 903-908.
[15]	HONG Yong. A Hilbert’s Type Series Inequality and Its Application [J]. J4, 2008, 46(02): 189-192.

Matching Parameter Conditions for the Best Hilbert-Type Integral Inequality with a Class of Non-homogeneous Kernels

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