Boundedness of rough fractional multilinear integral operators on generalized Morrey spaces

Abstract

We consider the boundedness of fractional multilinear integral operators with rough kernels T-A,T-m,(omega alpha) on the generalized Morrey spaces M-p,M-phi. We find the sufficient conditions on the pair (phi 1,phi 2), which ensures the boundedness of the operators T-A,T-m ,(omega alpha) from Mp,phi 1 to Mp,phi 2 for 1 < p < infinity. In all cases the conditions for the boundedness of the operator T-A,T-m (omega,alpha) is given in terms of Zygmund-type integral inequalities on (phi 1,phi 2), which do not make any assumption on the monotonicity of phi 1(x,r), phi 2(x,r) in r.