Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 027962, 17 pages
doi:10.1155/2007/27962
Research Article
On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel
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.
Abstract
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 ∥x∥αn (x∈ℝ+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.