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Zeitschrift für Analysis und ihre Anwendungen

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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