Title: Maximal operator for multilinear singular integrals with non-smooth kernels

Authors: Xuan Thinh Duong, Ruming Gong, Loukas Grafakos, Ji Li and Lixin Yan

Issue: Volume 58 (2009), Issue 6, 2517-2542

Abstract: In this article we prove Cotlar's inequality for the maximal singular integrals associated with operators whose kernels satisfy regularity conditions weaker than those of the standard $m$-linear Calder\'on-Zygmund kernels. The present study is motivated by the fundamental example of the maximal $m$-th order Calder\'on commutators whose kernels are not regular enough to fall under the scope of the $m$-linear Calder\'on-Zygmund theory; the Cotlar inequality is a new result even for these operators.