Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 47812, 9 pages
doi:10.1155/2007/47812
Research Article

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

Bicheng Yang

 Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China
Received 21 March 2007; Accepted 12 July 2007

Recommended by Shusen Ding

Abstract

Some character of the symmetric homogenous kernel of −1-order in Hilbert-type operator T:lr→lr (r>1) is obtained. Two equivalent inequalities with the symmetric homogenous kernel of −λ-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.