关于一个联系Riemann Zeta函数的Hilbert型积分不等式及逆式

On a Hilbert-Type Integral Inequality Related to Riemann's Zeta Function and Reverses

引入独立参量,应用实分析技巧及权函数的方法,建立一个最佳常数因子联系Riemann zeta函数的核含双曲余割函数的Hilbert型积分不等式,还考虑了其等价式、逆式与特殊参数下的非齐次形式.

By introducing a few independent parameters, applying the technique of real analysis and the way of weight functions, a new Hilbert-type integral inequality with the kernel containing hyperbolic cosecant function and a best constant factor related to Riemann＇s zeta function is given. The equivalent form, the reverses and the non-homogeneous forms for the particular parameter are considered.