Almost orthogonality and a class of bounded bilinear pseudodifferential operators

Several results and techniques that generate bilinear alternatives of a celebrated theorem of Calderón and Vaillancourt about the L 2 continuity of linear pseudodifferential operators with symbols with bounded derivatives are presented.The classes of bilinear pseudodifferential symbols considered are shown to produce continuous operators from L 2 × L 2 into L 1 .