Multilinear Commutators of Calderon-Zygmund Operator on Generalized Weighted Morrey Spaces

Abstract

The boundedness of multilinear commutators of Calderon-Zygmund operator T-(b) over right arrow on generalized weighted Morrey spaces M-p,M-phi(w) with the weight function w belonging to Muckenhoupt's class A(p) is studied. When 1 < p < infinity and (b) over right arrow - (b(1),...,b(m)), b(i) epsilon BMO i = 1,..., m, the sufficient conditions on the pair (phi(1), phi(2)) which ensure the boundedness of the operator T-(b) over right arrow from M-p,M-phi 1 (w) to M-p,M-phi 2 (w) are found. In all cases the conditions for the boundedness of T-(b) over right arrow are given in terms of Zygmund-type integral inequalities on (phi(1),phi(2)), which do not assume any assumption on monotonicity of phi(1) (x,r), phi(2) (x,r) in r.