Some Improvement on Hilbert's Inequality and Its Application

A new improvement of Hilbert's inequality for double series can be establishedby means of a strengthened Cauchy's inequality. As application, a quite sharp result onFejer-Riesz's inequality is obtained.

关于Hardy-Hilbert不等式的一个改进

本文研究关于重级数型Hardy-Hilbert不等式改进的问题.引入可变单位向量的概念,利用Gram矩阵的正定性创建了一个新的不等式.借助于Euler-Maclaurin求和公式,得到了Hardy-Hilbert不等式的结果.当p=2时,给出了经典的Hilbert重级数定理的一个改进.

Hardy-Hilbert重级数不等式的推广与改进

本文将著名的 Hardy-Hilbert重级数不等式∑∞m=1 ∑∞n=1ambnm + n≤ πsin(π/p) ∑∞n=1apn1p ∑∞n=1bqn1q∑∞m=1 ∑∞n=1anm + np ≤ πsin(π/p)p∑∞n=1apn进行了带参数形式的推广 。

逆向型Hilbert-Pachpatte不等式

建立了逆向型Hilbert-Pachpatte不等式,推广和改进了离散型和连续型Pach- patte不等式的逆.