# On the Hilbert Inequality With Weights

### Gao Mingzhe

Xiangxi Education College, Hunan, China### Wei Shongrong

Zhaqing College, Guangdong, China### He Leping

Xiangxi Education College, Hunan, China

## Abstract

In this paper, it is shown that a Hilbert-type inequality with weight $\omega(n) = \pi – \frac{\theta}{\sqrt{2n+1}}$ can be established where $\theta = \frac{17}{20}$. As application, a quite sharp result of the Hardy-Littlewood inequality is obtained and some further extensions are obtained.

## Cite this article

Gao Mingzhe, Wei Shongrong, He Leping, On the Hilbert Inequality With Weights. Z. Anal. Anwend. 21 (2002), no. 1, pp. 257–263

DOI 10.4171/ZAA/1077