Boundedness of rough fractional multilinear integral operators on generalized Morrey spaces

WOS: 000358613800002We 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.Ahi Evran University Scientific Research ProjectsAhi Evran University [PYO.FEN.4003.13.004, PYO.FEN.4001.14.006]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The authors are very grateful to the referees for their careful reading, comments, and suggestions, which helped us improve the presentation of this paper. The research of A Akbulut was partially supported by a grant of Ahi Evran University Scientific Research Projects PYO.FEN.4003.13.004 and PYO.FEN.4001.14.006. The research of Z Safarov was partially supported by a grant of Presidium Azerbaijan National Academy of Science 2015