非齐次核最佳半离散Hilbert型逆向不等式的等价条件及算子表示

Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (4): 823-830.

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Equivalent Conditions and Operator Expressions for the Best Half-Discrete Hilbert-Type Inverse Inequality with Non-homogeneous Kernel

HONG Yong¹, ZHANG Lijuan¹, KONG Yinying², LI Zhen²

1. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China;
2. College of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China

Received:2022-09-26 Online:2023-07-26 Published:2023-07-26

Abstract

Abstract: Firstly, by using the power function method, we discussed the half-discrete Hilbert-type inverse inequality with non-homogeneous kernel K(n,x)=G(n^λ1x^λ2)(λ₁λ₂>0), gave equivalent conditions for the best half-discrete Hilbert-type inverse inequality and the relationship between the parameters. Secondly, as an application, we gave the equivalent operator expressions and some special cases.

Key words: non-homogeneous kernel, half-discrete Hilbert-type inverse inequality, the best constant factor, operator expression, Beta function

CLC Number:

O178

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.

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Equivalent Conditions and Operator Expressions for the Best Half-Discrete Hilbert-Type Inverse Inequality with Non-homogeneous Kernel

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