Different versions of the Hilbert inequality has been investigated by many mathematicians, see [A. Kufner
, L. Maligranda
and L.-E. Persson
, The Hardy inequality. About its history and some related results, Pilsen: Vydavatelský Servis (2007; Zbl 1213.42001
)]. Utilizing the properties of rearrangement of a function, the authors present some Hilbert type inequalities with non-conjugate parameters and by using a new analytic technique they find the best possible constants in these inequalities.