一个含有复合核的Hilbert型不等式

On a Hilbert-type Inequality Involving a Composite Kernel

通过引入恰当参数,构建一个与对数函数相关联并同时包含齐次和非齐次两种情形的核函数.借助实分析的相关技巧,建立一个含最佳常数因子的Hilbert型积分不等式.特别地,作为结论的应用,通过对参数赋予特殊值,文末还建立了若干推论.

By introducing several parameters,this paper constructs a composite kernel function which is associated with logarithmic function and contains both homogeneous and non-homogeneous cases.With the help of real analysis techniques,a Hilbert-type integral inequality with optimal constant factor is established.In particular,as an application of the conclusion,some inferences are established by assigning special values to parameters.