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The Scientific World Journal
Volume 2014, Article ID 169061, 8 pages
http://dx.doi.org/10.1155/2014/169061
Research Article

Parameterized Hilbert-Type Integral Inequalities in the Whole Plane

1Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China
2Department of Mathematics and Computer Science, Longyan University, Longyan, Fujian 364012, China

Received 21 June 2014; Accepted 5 August 2014; Published 19 August 2014

Academic Editor: Tohru Ozawa

Copyright © 2014 Qiliang Huang et al. 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 the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels.