Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 027962, 17 pages
Research Article

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

Wuyi Zhong and Bicheng Yang

Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China

Received 26 April 2007; Accepted 29 August 2007

Academic Editor: Sever S. Dragomir

Copyright © 2007 Wuyi Zhong and Bicheng Yang. 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.


We build a multiple Hilbert-type integral inequality with the symmetric kernel K(x,y) and involving an integral operator T. For this objective, we introduce a norm xαn(x+n), two pairs of conjugate exponents (p,q) and (r,s), 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.