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

Abstract

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 Mpw,? (Rn). We study the boundedness of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and g*? -function and their higher order commutators on vector-valued generalized weighted Morrey spaces Mpw,? (l2). In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on ?(x,r) without assuming any monotonicity property of ?(x, r) in r. © 2010 AZJM All rights reserved.