In this paper, we build a new Hilbert's inequality with the homogeneous kernel of real order and the integral in whole plane. The equivalent inequality is considered. The best constant factor is calculated using ψ function.
Bulletin of Mathematical Sciences and Applications (Volume 3)
Z. T. Xie et al., "A New Hilbert-Type Integral Inequality with the Homogeneous Kernel of Real Degree Form and the Integral in Whole Plane", Bulletin of Mathematical Sciences and Applications, Vol. 3, pp. 71-82, 2013