Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 401428, 11 pages
Research Article

A Hilbert-Type Integral Inequality in the Whole Plane with the Homogeneous Kernel of Degree −2

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

Received 20 December 2010; Accepted 29 January 2011

Academic Editor: S. Al-Homidan

Copyright © 2011 Dongmei Xin and 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.


By applying the way of real and complex analysis and estimating the weight functions, we build a new Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree −2 involving some parameters and the best constant factor. We also consider its reverse. The equivalent forms and some particular cases are obtained.