Multilinear commutators of Calderón-Zygmund operator on generalized weighted morrey spaces

The boundedness of multilinear commutators of calderón-zygmund operator t→b on generalized weighted morrey spaces m p,φ(w) with the weight function w belonging to muckenhoupt's class a p 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 t→b from m p,φ1(w) to m p,φ2(w) are found. in all cases the conditions for the boundedness of t→b 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. copyright © 2014 v. s. guliyev and f. ch. alizadeh.