JournalszaaVol. 21, No. 1pp. 257–263

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
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Abstract

In this paper, it is shown that a Hilbert-type inequality with weight ω(n)=πθ2n+1\omega(n) = \pi – \frac{\theta}{\sqrt{2n+1}} can be established where θ=1720\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