The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (179 KB) | Metadata | Table of Contents | ZAA summary
Volume 21, Issue 1, 2002, pp. 257–263
DOI: 10.4171/ZAA/1077

Published online: 2002-03-31

On the Hilbert Inequality With Weights

Gao Mingzhe[1], Wei Shongrong[2] and He Leping[3]

(1) Xiangxi Education College, Hunan, China
(2) Zhaqing College, Guangdong, China
(3) Xiangxi Education College, Hunan, China

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.

Keywords: Hilbert inequality with weights, Hardy-Littlewood inequality, infimum, weight functions

Mingzhe Gao, Shongrong Wei, Leping He: On the Hilbert Inequality With Weights. Z. Anal. Anwend. 21 (2002), 257-263. doi: 10.4171/ZAA/1077