一个复合核Hilbert型不等式的推广

On an Extension of a Hilbert-type Inequality Involving a Compound Kernel

通过引进若干参数,构造一个同时含有指数函数和对数函数、并且包含齐次型和非齐次型两种形态的复合型核函数.借助分析学的有关技巧,对齐次型和非齐次型两种情形采用统一的处理方式,从而建立一个新的Hilbert型积分不等式,并给出了最佳常数因子.特别地,作为结论的应用,对参数赋予一些特殊数值,文末建立了一些推论.

By introducing some parameters,a compound kernel function with exponential function and loga-rithmic function,including two cases of homogeneous and non-homogeneous is constructed.With the help of some analysis techniques,and using a unified treatment of homogeneous and non-homogeneous cases,a new Hil-berttype integral inequality is established,and the constant factor is proved to be the best possible.As an applica-tion of the conclusion,some special values are given to the parameters,and some corollaries are established at the end of the paper.