Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels T-Omega,alpha(A1,A2,...,Ak), which is a generalization of the higher- order commutator of the rough fractional integral on the generalized weighted Morrey spaces M-p,M-phi(w). We find the sufficient conditions on the pair (phi(1),phi(2) ) with w is an element of A(p),(q) which ensures the boundedness of the operators T-Omega,alpha(A1,A2,...,Ak) from M-p,M-phi(w). In all cases the conditions for the boundedness of the operator T-Omega,alpha(A1,A2,...,Ak) are given in terms of Zygmund-type integral inequalities on.' 1; ' 2/ and w, which do not assume any assumption on monotonicity of phi 1(x,r), phi 2(x,r) in r.