Weighted norm inequalities for multilinear singular integral operators and applications

In this paper, weighted norm inequalities with $A_p$ weights are established for the multilinear singular integral operators whose kernels satisfy $L^{r^{\mathrm{\prime }}}$-H"ormander regularity condition. As applications, we recover a weighted estimate for the multilinear Fourier multiplier obtained by Fujita and Tomita, and obtain several new weighted estimates for the multilinear Fourier multiplier as well.