By establishing the weight function, we present a new Hilbert-type inequality with the integral in whole plane and with a best constant factor, and its kernel is a homogeneous form of degree-3, and also we put forward its equivalent form.
The Bulletin of Society for Mathematical Services and Standards (Volume 4)
Z. T. Xie and Z. Zheng, "A Hilbert-Type Integral Inequality with the Homogeneous Kernel of Degree-3 and a Best Constant Factor", The Bulletin of Society for Mathematical Services and Standards, Vol. 4, pp. 41-46, 2012