拟齐次核的Hilbert型级数不等式的最佳搭配参数条件及应用

Abstract

Abstract:

Choosing $a, b$ as the matching parameters, we can sue the weight function method to obtain Hilbert-type series inequality $\sum\limits_{m=1}^{\infty}\sum\limits_{n=1}^{\infty}K(m, n)a_{m}b_{n}\leq M(a, b)\|\tilde{a}\|_{p, \alpha(a, b)}\|\tilde{b}\|_{q, \beta(a, b)}.$ in the paper, the problem of how to choose $a, b$ in order to make $M(a, b)$ the best constant factor in inequality with quasi-homogeneous kernels are discussed, necessary and sufficient conditions are obtained for $a, b$ to the best matching parameters, the formula for the best constant factor is obtained. Finally, their applications to solving operator morn are discussed.

Key words: Hilbert-type series inequality, Quasi-homogeneous kernel, The best constant factor, The best matching parameter, Operator norm

CLC Number:

O178

Yong Hong,Qiang Chen. The Best Matching Parameters Conditions of Hilbert-Type Series Inequality with Quasi-Homogeneous Kernel and Applications[J].Acta mathematica scientia,Series A, 2022, 42(1): 26-34.

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References 13

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The Best Matching Parameters Conditions of Hilbert-Type Series Inequality with Quasi-Homogeneous Kernel and Applications

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