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 X ⋯ X 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.
|Number of pages||25|
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - Apr 2010|