Open Access

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

Journal of Inequalities and Applications20082008:917392

https://doi.org/10.1155/2008/917392

Received: 24 March 2008

Accepted: 19 May 2008

Published: 20 May 2008

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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Authors’ Affiliations

(1)
Department of Mathematics, Guangdong Institute of Education

Copyright

© Wuyi Zhong. 2008

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.