  In this paper, the weighted estimates for multilinear pseudo-differential
operators were systematically studied in rearrangement invariant Banach and
quasi-Banach spaces. These spaces contain the Lebesgue space, the classical
Lorentz space and Marcinkiewicz space as typical examples. More precisely, the
weighted boundedness and weighted modular estimates, including the weak
endpoint case, were established for multilinear pseudo-differential operators
and their commutators. As applications, we show that the above results also
hold for the multilinear Fourier multipliers, multilinear square functions, and
a class of multilinear Calder\'{o}n-Zygmund operators.
