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.
The Bulletin of Society for Mathematical Services and Standards (Volume 5)
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", The Bulletin of Society for Mathematical Services and Standards, Vol. 5, pp. 49-59, 2013