Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 158690, 12 pages
Research Article

An Extension of the Hilbert's Integral Inequality

Department of Mathematics and Computer Science, Normal College of Jishou University, Hunan Jishou 416000, China

Received 30 May 2009; Accepted 20 August 2009

Academic Editor: Wing-Sum Cheung

Copyright © 2009 Zhou Yu et al. 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.


It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters m (mN) and λ (λ>0). The constant factors expressed by the Euler number and π as well as by the Bernoulli number and π, respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.