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On new extensions of Hilbert’s integral inequality. (English) Zbl 1153.26006

Authors’ abstract: It is shown that some new extensions of Hilbert’s integral inequality with parameter \(\lambda (\lambda >1/2)\) can be established by introducing a proper weight function. In particular, when \(\lambda =1\), a refinement of Hilbert’s integral inequality is obtained. As applications, some new extensions of Widder’s inequality and Hardy-Littlewood’s inequality are given.

MSC:

26D15 Inequalities for sums, series and integrals
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References:

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