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On Hilbert's Inequality for Double Series and Its Applications

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  • Zhou Yu
  • Gao Mingzhe

Abstract

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function and a parameter . In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality in function are given.

Suggested Citation

  • Zhou Yu & Gao Mingzhe, 2008. "On Hilbert's Inequality for Double Series and Its Applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-12, April.
    • Handle: RePEc:hin:jijmms:165089
    DOI: 10.1155/2008/165089
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