Rough Fractional Multilinear Integral Operators on Generalized Weighted Morrey Spaces

In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels T-Omega,alpha(A,m) 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)(R-n) which ensures the boundedness of the operators T-Omega,alpha(A,m) from M-p,M-phi 1 (w) to M-p,M-phi 2 (w) for 1 < p < infinity. In all cases the conditions for the boundedness of the operator T-Omega,alpha(A,m) is given in terms of Zygmund-type integral inequalities on (phi(1), phi(2)) and w, which do not assume any assumption on monotonicity of phi(1) (x, r), phi(2) (x, r) in r.