The Adaptation Parameter Conditions for Hilbert-type Integral Inequalities with Quasi-homogeneous Kernels

ZENG Zhihong; HONG Yong; ZHANG Ranran; TIAN Delu

doi:10.6054/j.jscnun.2021082

Journal of South China Normal University (Natural Science Edition) > 2021 > 53(5): 108-112. > DOI: 10.6054/j.jscnun.2021082

ZENG Zhihong, HONG Yong, ZHANG Ranran, TIAN Delu. The Adaptation Parameter Conditions for Hilbert-type Integral Inequalities with Quasi-homogeneous Kernels[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(5): 108-112. DOI: 10.6054/j.jscnun.2021082

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The Adaptation Parameter Conditions for Hilbert-type Integral Inequalities with Quasi-homogeneous Kernels

1.
Editorial Department of Journal, Guangdong University of Education, Guangzhou 510303, China
2.
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
3.
School of Mathematics, Guangdong University of Education, Guangzhou 510303, China

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Received Date: November 29, 2020
Available Online: November 10, 2021

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Abstract

The weighting coefficient method and real analysis techniques are used to discuss how to select the adaptation parameters to obtain Hilbert-type integral inequalities with quasi-homogeneous kernel and the best constant factor. The necessary and sufficient conditions for the adaptation parameters for constructing the best Hilbert-type integral inequality with quasi-homogeneous kernel and the expression formula of the best constant factor are obtained. This solves a fundamental theoretical problem in the study of constructing optimal Hilbert-type integral inequalities. Finally, its applications to finding the norm of integration operators are discussed.

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