Multilinear commutators of vector-valued intrinsic square functions on vector-valued generalized weighted Morrey spaces

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spaces M-w(p,phi) (l(2)). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and g(lambda)* -function, and their multilinear commutators on vector-valued generalized weighted Morrey spaces M-w(p,phi) (l(2)). In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on phi(x, r) without assuming any monotonicity property of phi(x, r) on r.