By using the weight functions and by means of Hadamard's inequality, we present a new Hilbert-type inequality with the integral in whole plane, a best constant factor and a homogeneous kernel of degree-2.
Bulletin of Mathematical Sciences and Applications (Volume 7)
Z. Zheng et al., "A New Hilbert-Type Inequality with the Homogeneous Kernel of Degree - 2 and with the Integral", Bulletin of Mathematical Sciences and Applications, Vol. 7, pp. 9-17, 2014