Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 256796, 8 pages
doi:10.1155/2010/256796
Research Article

On a New Hilbert-Type Intergral Inequality with the Intergral in Whole Plane

Zheng Zeng1 and Zitian Xie2

1Department of Mathematics, Shaoguan University, Shaoguan, Guangdong 512005, China
2Department of Mathematics, Zhaoqing University, Zhaoqing, Guangdong 526061, China

Received 5 May 2010; Accepted 14 July 2010

Academic Editor: Andrea Laforgia

Copyright © 2010 Zheng Zeng and Zitian Xie. 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

By introducing some parameters and estimating the weight functions, we build a new Hilbert's inequality with the homogeneous kernel of 0 order and the integral in whole plane. The equivalent inequality and the reverse forms are considered. The best constant factor is calculated using Complex Analysis.