We obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard Calderón-Zygmund kernels. As a consequence, we deduce endpoint L¹ ×···×L¹ to weak L¹/m estimates for the mth-order commutator of Calderón. Our results reproduce known estimates for m = 1, 2 but are new for m ≥ 3. We also explore connections between the 2nd-order higher-dimensional commutator and the bilinear Hilbert transform and deduce some new off-diagonal estimates for the former.
Copyright 2010 American Mathematical Society. First published in Transactions of the American Mathematical Society, Vol.362, No. 4, published by the American Mathematical Society. The original article can be found at http://www.ams.org/journals/tran/