曾志红, 洪勇, 张然然, 田德路. 拟齐次核的Hilbert型积分不等式的适配参数条件[J]. 华南师范大学学报(自然科学版), 2021, 53(5): 108-112. doi: 10.6054/j.jscnun.2021082
引用本文: 曾志红, 洪勇, 张然然, 田德路. 拟齐次核的Hilbert型积分不等式的适配参数条件[J]. 华南师范大学学报(自然科学版), 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
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

拟齐次核的Hilbert型积分不等式的适配参数条件

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

  • 摘要: 利用权系数方法和实分析技巧,讨论如何选取适配参数而获得具有最佳常数因子的拟齐次Hilbert型积分不等式,得到构建最佳拟齐次Hilbert型积分不等式的适配参数的充分必要条件,并得到最佳常数因子的表达式,从而解决了构建最佳Hilbert型积分不等式研究中的一个基本理论问题;最后讨论所得结论在求积分算子范数中的应用.

     

    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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