Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 27962, 17 pages
doi:10.1155/2007/27962
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

Recommended by Sever S. Dragomir

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.