齐次核的Hilbert型积分不等式的研究进展与现状

Research Progress and Present Situation of Hilbert-type Integral Inequality with Homogeneous Kernel

对齐次核的Hilbert型积分不等式的研究方法和理论意义进行陈述,讨论研究进展与研究现状.按研究的深度,将研究进展分为3个阶段:以针对具体齐次核进行适当的参数搭配得到最佳不等式为特征的第一阶段;以针对抽象齐次核寻求不等式取最佳常数因子的等价参数条件为特征的第二阶段;针对抽象齐次核寻求不等式成立的充要条件的第三阶段.通过这3个阶段的划分,有助于了解Hilbert型不等式的研究现状.

This paper makes a statement on the research method and theoretical meaning of Hilbert-type integral inequality with Homogeneous kernel,the research progress and current situation are discussed.According to the depth of the research,the research progress is divided into three stages.The first stage is characterized by getting the best inequality by proper parameter collocation for specific homogeneous kernel.The feature of the second stage is to get the best constant factor of inequality by proper parameter collocation for abstract homogeneous kernel.The third stage is characterized by seeking the necessary and sufficient condition for the existence of inequalities with the abstract homogeneous kernel.The division of these three stages is helpful to understand the current situation of Hilbert-type inequality research.