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

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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 MΦ,φw(Rⁿ). We study the boundedness of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and gλ* -function and their commutators on vector-valued generalized weighted Morrey spaces MΦ,φw(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.