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.

Abstract

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.