  In this paper, we prove the boundedness of the multilinear Littlewood-Paley
square operators and their commutators on weighted Morrey spaces, then we give
the boundedness and weak-type $L\log L$ estimates for the commutators of
multilinear Littlewood-Paley g-functions and multilinear Marcinkiewicz
integrals on weighted Morrey spaces in the form of corollaries.
