By applying the weight functions, the idea of introducing parameters and the technique of real analysis, a new multiple Hilbert-type integral inequality involving the upper limit functions is given. The constant factor related to the gamma function is proved to be the best possible in a condition. A corollary about the case of the nonhomogeneous kernel and some particular inequalities are obtained.

中文翻译：

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关于涉及上限函数的多个希尔伯特型积分不等式

通过应用加权函数，引入参数的思想和实分析技术，给出了一个新的涉及上限函数的多重希尔伯特型积分不等式。在某种情况下，与伽玛函数有关的常数被证明是最好的。得到关于非均质核的情况和某些特定不等式的推论。