Open Access

On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of 1-Order and Applications

Journal of Inequalities and Applications20072007:047812

https://doi.org/10.1155/2007/47812

Received: 21 March 2007

Accepted: 12 July 2007

Published: 25 October 2007

Abstract

Some character of the symmetric homogenous kernel of 1-order in Hilbert-type operator is obtained. Two equivalent inequalities with the symmetric homogenous kernel of -order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.

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Authors’ Affiliations

(1)
Department of Mathematics, Guangdong Institute of Education

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Copyright

© Bicheng 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.