Discrete decompositions for bilinear operators and almost diagonal conditions

Using discrete decomposition techniques, bilinear operators are naturally a ssociated with trilinear tensors. An intrinsic size condition on the entrie s of such tensors is introduced and is used to prove boundedness for the co rresponding bilinear operators on several products of function spaces. This condition should be considered as the direct analogue of an almost diagona l condition for linear operators of Calderon-Zygmund type. Applications inc lude a reduced T1 theorem for bilinear pseudodifferential operators and the extension of an L-p multiplier result of Coifman and Meyer to the full ran ge of H-p spaces. The results of this article rely on decomposition techniq ues developed by Frazier and Jawerth and on the vector valued maximal funct ion estimate of Fefferman and Stein.