Eroglu A.Isayev F.A.Namazov F.M.2019-08-012019-08-0120182306-2193https://hdl.handle.net/11480/1731Let L = -?Hn + V be a Schrödinger operator on the Heisenberg groups Hn, where the nonnegative potential V belongs to the reverse Hölder class RHQ/2 and Q is the homogeneous dimension of Hn. Let b belong to a newBMO?(Hn, ?) space, and let IL ß be the fractional integral operator associated with L. In this paper, we study the boundedness of the operator IL ß and its commutators [b, IL ß ] with b ? BMO?(Hn, ?) on vanishing generalized Morrey spaces VM?,V p,? (Hn) associated with Schrödinger operator. We find the sufficient conditions on the pair (?1, ?2) which ensures the boundedness of the operator IL ß from VM?,V p,?1 (Hn) to LM?,V q,?2 (Hn), 1/p - 1/q = ß/Q. When b belongs to BMO?(Hn, ?) and (?1, ?2) satisfies some conditions, we also show that the commutator operator [b, IL ß ] are bounded from VM?,V p,?1 (Hn) to VM?,V q,?2 (Hn), 1/p - 1/q = ß/Q. © 2018, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.eninfo:eu-repo/semantics/closedAccessBmoCommutatorFractional integralHeisenberg groupSchrödinger operatorVanishing generalized morrey spaceArticle38454622-s2.0-85067987376Q3