Department of Mathematics, Guangdong Institute of Education, Guangzhou, Guangdong 510303, China
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.
A Hilbert-type linear operator 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.