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On a New Generalization of Hilbert's Integral Inequality and its Applications

Bicheng Yang, L. Debnath

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Abstract

This paper deals with a new generalization of Hilbert's integral inequality with a best possible constant factor involving the β function. As applications, general inequalities equivalent to Hilbert's type inequality and Hardy-Littlewood's integral inequality are proved.

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This paper deals with a new generalization of Hilbert's integral inequality with a best possible constant factor involving the β function. As applications, general inequalities equivalent to Hilbert's type inequality and Hardy-Littlewood's integral inequality are proved.

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Available abstract

This paper deals with a new generalization of Hilbert's integral inequality with a best possible constant factor involving the β function. As applications, general inequalities equivalent to Hilbert's type inequality and Hardy-Littlewood's integral inequality are proved.

Key concepts: Mathematics, Kantorovich inequality, Generalization, Hölder's inequality, Inequality, Rearrangement inequality, Log sum inequality, Bessel's inequality

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