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

Abstract

The boundedness of multilinear commutators of Calderón-Zygmund operator Tb→ 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 b→=(b1,…,bm), bi∈BMO, i=1,…,m, the sufficient conditions on the pair (φ1,φ2) which ensure the boundedness of the operator Tb→ from Mp,φ1(w) to Mp,φ2(w) are found. In all cases the conditions for the boundedness of Tb→ are given in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity of φ1(x,r), φ2(x,r) in r.