On General multilinear square function with non-smooth kernels

Preprint, 2015

In this paper, we obtain some boundedness of multilinear square functions $T$ with non-smooth kernels which extend some known results significantly. We also introduce the multilinear maximal square function $T^*$ and weighted strong and weak type estimates for $T^*$ are given. % As applications, we deduce some weighted estimates for Calder\'on commutator and multilinear Littlewood-paley operator.