一个具多参数核为双曲余切函数的积分不等式

A Integral Inequality with Multi-parameters and the Kernel of Hyperbolic Cotangent Function

应用权函数方法和实分析技巧,引入多参数和一些特殊函数联合刻划常数因子,得到了一个多参数Hilbert型积分不等式,考虑了其等价形式,并证明它们的常数因子是最佳的,同时得到了一个有用的多参数核为双曲余切函数的积分不等式.

In this paper, by using the way of weight function and the technique of real analysis, and introducing some parameters and some special functions to jointly characterize the constant factor, a multi-parameters Hilbert-type integral inequality is given. It＇s equivalent form is considered and their constant factors are proved being the best possible. At the same time, a useful multi-parameters integral inequality with the kernel of hyperbolic cotangent function is obtained.