Maximal operator for multilinear singular integrals with non-smooth kernels

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 Calderón-Zygmund kernels. The present study is motivated by the fundamental example of the maximal mth order Calderón commutators whose kernels are not regular enough to fall under the scope of the m-linear Calderón-Zygmund theory; the Cotlar inequality is a new result even for these operators.