一类新的带参数的Hilbert 型积分不等式

A New Hilbert-Type Integral Inequality with Parameters

中文关键词:  Hilbert型积分不等式  双曲余割函数  Bernoulli 数  权函数  最佳常数．

英文关键词:Hilbert-type integral inequality  hyperbolic cosecant function  Bernoulli number  weight function  best constant.

中文摘要:

      通过引入两个参数$m$ ($m \in N)$ 和 $\lambda$($\lambda>0)$.建立了一类新的Hilbert型不等式.证明了用Bernoulli数和$\pi$所表示的常数因子是最佳的,列举了若干重要的特殊结果.作为应用,给出了一些等价形式．

英文摘要:

      In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters $m~(m \in N)$ and $\lambda~(\lambda > 0)$. And the constant factor expressed by the Bernoulli number and $\pi$ is proved to be the best possible. And then some important and especial results are enumerated. As applications, some equivalent forms are given.