A Hilbert-type integral inequality whose kernel is a homogeneous form of degree \(-3\) (Q2465144)

The authors establish direct and reverse Hilbert-type inequalities involving the integral \[ \int_0^\infty\int_0^\infty\frac{f(x)g(y)}{(x+a^2y)(x+b^2y)(x+c^2y)}\,dx\,dy \] In both cases best constants are provided.