FRACTIONAL INTEGRAL ASSOCIATED WITH SCHRODINGER OPERATOR ON VANISHING GENERALIZED MORREY SPACES

WOS: 000445366500015Let L= -Delta + V be a Schrodinger operator, where the non-negative potential V belongs to the reverse Holder class RHn/2, let b belong to a new BMO theta(rho) space, and let I-beta(L) be the fractional integral operator associated with L. In this paper, we study the boundedness of the operator I-beta(L) and its commutators [b, I-beta(L)] with b is an element of BMO theta(rho) on generalized Morrey spaces associated with Schrodinger operator M-p,phi(alpha,V) and vanishing generalized Morrey spaces associated with Schrodinger operator VMp,phi alpha,V. We find the sufficient conditions on the pair (phi(1), phi(2)) which ensures the boundedness of the operator I-beta(L) from M-p,phi 1(alpha,V) to M-q,phi 2(alpha,V) and from VMp,phi 1 alpha,V to VMq,phi 2 alpha,V, 1/p - 1/q = beta/n. When b belongs to BMO theta(rho) and (phi(1), phi(2)) satisfies some conditions, we also show that the commutator operator [b, I-beta(L)] is bounded from M-p,phi 1(alpha,V) to M-q,phi 2(alpha,V) and from VMp,phi 1 alpha,V to VMq,phi 2 alpha,V, 1/p - 1/q = beta/n.Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.023]; Presidium of Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)We thank the referee(s) for careful reading the paper and useful comments. The research of A. Akbulut was partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.023). The research of M. Omarova was partially supported by the grant of Presidium of Azerbaijan National Academy of Science 2015