Open Access

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

Journal of Inequalities and Applications20072007:027962

DOI: 10.1155/2007/27962

Received: 26 April 2007

Accepted: 29 August 2007

Published: 13 November 2007

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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Authors’ Affiliations

(1)
Department of Mathematics, Guangdong Institute of Education

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Copyright

© W. Zhong and B. Yang 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.