... original work is properly cited.By introducing some parameters and estimating the weight functions, we build a new Hilbert’sinequality with the homogeneous kernel of 0 order and the integral in ... S. Mitrinovi´c, J. E. Peˇcari´c, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, vol. 53, Kluwer Academic, Boston, Mass, USA, 1991.4 Z. Xie and Z. ... contradicts the fact thath<k. Hence the constant k in 3.1 is the best possible.Thus we complete the proof of the theorem.Journal of Inequalities and Applications 5Setting y tx thenI1...