Multilinear Commutators of Calderón-Zygmund Operator on Generalized Weighted Morrey Spaces.

The boundedness of multilinear commutators of Calderón-Zygmund operator T... on generalized weighted Morrey spaces Mp,φ(w) with the weight function w belonging to Muckenhoupt's class Ap is studied. When 1 < p < ∞ and ... = (b1,..., bm), bi ∈ BMO, i = 1,..., m, the sufficient conditions on the pair (φ1, φ2) which ensure the boundedness of the operator T... from Mp,φ1 (w) to Mp,φ2 (w) are found. In all cases the conditions for the boundedness of T... are given in terms of Zygmund-type integral inequalities on ((φ 1,φ2), which do not assume any assumption on monotonicity of φ1 (x, r), φ2 (x,r) in r. [ABSTRACT FROM AUTHOR]