Higher Order 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 analogues of intrinsic square functions in the generalized weighted Morrey spaces M-w(p,phi) (R-n). We study the boundedness of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and g(lambda)(*)-function and their higher order 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 in terms of Zygmund-type integral inequalities on phi(x, r) without assuming any monotonicity property of phi(x, r) in r.