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ON THE HILBERT INEQUALITY AND ITS APPLICATIONS
2009
In this paper, a new refinement of the Hilbert inequality for double series can be established by means of Euler-Maclaurin summation and by introducing a proper weight function. A similar result for the Hilbert integral inequality is also proved. As applications, some strengthened results of the Hardy-Littlewood theorem and the Widder theorem are given.
Keywords:
- Hilbert's basis theorem
- Hilbert's second problem
- Hilbert's fourteenth problem
- Log sum inequality
- Mathematical analysis
- Rearrangement inequality
- Gronwall's inequality
- Discrete mathematics
- Bessel's inequality
- Hilbert manifold
- Mathematics
- Reproducing kernel Hilbert space
- Hölder's inequality
- Kantorovich inequality
- Pure mathematics
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