JMAT_V4_N3_RP3 Zheng Zeng Zitian Xie Journal on Mathematics 2277-5137 4 3 25 34 Multiple Hilbert-Type Integral Inequality, Weight Function, Holder's Inequality, Non-Homogeneous Form Hilbert-type inequalities are important in analysis and its applications. In recent years, some authors have studied and published a few Hilbert-type multiple integral inequalities, which are hard and interesting. In this paper, by estimating the weight function and technique of real analysis, the authors give a new multiple Hilbert-type integral inequality with a non-Homogeneous form as, F(x,y) f(x)g(y)dxdy < K f g (p >1). The best possible Rn+ x Rn+ p,w q,w constant factor is given, and the equivalent form is also considered. Many particular cases of Hilbert-type integral inequality with a non-homogeneous form are included. As its applications, the authors have considered some particular results. July - September 2015 Copyright © 2015 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=3597