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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
Citation: 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

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

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