Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 494257, 18 pages
doi:10.1155/2009/494257
Research Article

A Hilbert-Type Linear Operator with the Norm and Its Applications

Wuyi Zhong

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

Received 9 February 2009; Accepted 9 March 2009

Academic Editor: Nikolaos Papageorgiou

Copyright © 2009 Wuyi Zhong. 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

A Hilbert-type linear operator T:ℓϕp→ℓψp is defined. As for applications, a more precise operator inequality with the norm and its equivalent forms are deduced. Moreover, three equivalent reverses from them are given as well. The constant factors in these inequalities are proved to be the best possible.