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The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of -Degree

Abstract

By introducing an integral operator, a norm with a weight function, and two pairs of conjugate exponents, we find the conditions for the Hilbert-type integral inequalities with a homogeneous kernel of -degree. We also prove that the constant factors in the inequalities are all the best possible. As the particular situations, some new inequalities with a homogeneous kernel and their other two forms are given. We extend some previous results.

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Correspondence to Wuyi Zhong.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhong, W. The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of -Degree. J Inequal Appl 2008, 917392 (2008). https://doi.org/10.1155/2008/917392

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