Bilinear interpolation theorems and applications

Interpolation of bilinear operators is studied. The celebrated Littlewood mixed norm inequality is used to prove interpolation theorems for bilinear operators defined on couples of c0-weighted sequence spaces generated by parameters of quasi-concave functions. It is shown that these results can be lifted to a wider class of abstract methods of interpolation. The abstract results are used to prove bilinear interpolation theorems to the setting of Calderón–Lozanovskii spaces. As an application the boundedness of the bilinear Hilbert transform between Orlicz spaces including Zygmund classes is proved.