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On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel

Abstract

We build a multiple Hilbert-type integral inequality with the symmetric kernel and involving an integral operator. For this objective, we introduce a norm, two pairs of conjugate exponents and, and two parameters. As applications, the equivalent form, the reverse forms, and some particular inequalities are given. We also prove that the constant factors in the new inequalities are all the best possible.

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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., Yang, B. On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel. J Inequal Appl 2007, 027962 (2007). https://doi.org/10.1155/2007/27962

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Keywords

  • Integral Operator
  • Constant Factor
  • Equivalent Form
  • Integral Inequality
  • Reverse Form
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