关于一个联系Riemann Zeta函数的Hilbert型积分不等式及逆式

摘要

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.