Maximal operator for multilinear singular integrals with non-smooth kernels Xuan DuongRuming GongLoukas GrafakosJi LiLixin Yan 42B2042B2546B7047G30multilinear singular integralsmaximal operatorCotlar's inequalityweighted norm inequalitiesgeneralized Calder\'on-Zygmund operatorcommutators 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. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3803 10.1512/iumj.2009.58.3803 en Indiana Univ. Math. J. 58 (2009) 2517 - 2542 state-of-the-art mathematics http://iumj.org/access/