一个经典Hilbert型不等式的再推广

On a Generalization of a Classical Hilbert-type Integral Inequality

通过新引入若干个参数,构建了一个在第一象限内定义的齐次核函数,由此建立了一个常数因子最佳的Hilbert型积分不等式.并且可以证明这一新建立的结果是一个经典的Hilbert型不等式的推广.此外,借助余切函数的有理分式展开给出了最佳常数因子的简洁表达.最后,通过对参数赋予不同数值,文末给出了一些有趣的推论.

By introducing some new parameters,and constructing a homogeneous kernel function defined in the first quadrant,we establish a new Hilbert-type integral inequality and generalize a classical result.meanwhile,by using the rational fraction expansion of cotangent function,we present the representation of the best possible constant factor concisely.Moreover,giving the parameters special values,some new results of interest are presented at the end of the paper.