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 Mwp,φ(l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ∗ -function, and their multilinear commutators on vector-valued generalized weighted Morrey spaces Mwp,φ(l2). In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on φ(x,r) without assuming any monotonicity property of φ(x,r) on r.