中文摘要：

本文利用权函数方法和实分析技巧,引入Gamma函数和推广的Zeta函数联合刻划常数因子,得到一个混合核Hilbert型积分不等式和它的等价式,并证明它们的常数因子是最佳值.作为应用,通过选取特殊参数值获得一些有意义的结果.另一方面,改进参考文献中的一些相关结果.

英文摘要：

In this paper, by means of weight function and the technique of real analysis, and introducing F- function and the generalized ζ- function to characterize the constant factor jointly, a Hilbcrt-type integral inequality with the mixed kernel and it＇s equivalent form are given. Their constant factors are proved being the best possible. As for applications, some meaningful results are obtained by selecting the special parameter values, and the results in the related references are promoted.