Grafakos, LoukasTorres, Rodolfo H.2015-03-262015-03-262002-10-23Grafakos, Loukas & Torres, Rodolfo "Discrete decompositions for bilinear operators and almost diagonal conditions." Trans. Amer. Math. Soc. 354 (2002), 1153-1176. http://dx.doi.org/10.1090/S0002-9947-01-02912-9.https://hdl.handle.net/1808/17228This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9947-01-02912-9. First published in Transaction of American Mathematical Society in 2002, published by the American Mathematical Society.Using discrete decomposition techniques, bilinear operators are naturally associated with trilinear tensors. An intrinsic size condition on the entries of such tensors is introduced and is used to prove boundedness for the corresponding bilinear operators on several products of function spaces. This condition should be considered as the direct analogue of an almost diagonal condition for linear operators of Calderón-Zygmund type. Applications include a reduced $T1$ theorem for bilinear pseudodifferential operators and the extension of an $L^p$ multiplier result of Coifman and Meyer to the full range of $H^p$ spaces. The results of this article rely on decomposition techniques developed by Frazier and Jawerth and on the vector valued maximal function estimate of Fefferman and Stein.Singular integralsmaximal functionsLittlewood-Paley theoryalmost diagonal conditionmultilinear operatorswaveletsTriebel-Lizorkin spacesArticle10.1090/S0002-9947-01-02912-9openAccess