Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 047812, 9 pages
doi:10.1155/2007/47812
Research Article
On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of −1-Order and Applications
Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China
Received 21 March 2007; Accepted 12 July 2007
Academic Editor: Shusen Ding
Copyright © 2007 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
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.