Marcinkiewicz integrals with rough kernel associated with Schrodinger operators and commutators on generalized vanishing local Morrey spaces

Let L = -Delta + V (x) be a Schrodinger operator, where Delta is the Laplacian on R-n, while nonnegative potential V (x) belonging to the reverse Holder class. In this paper, using the some conditions on phi (x.r), we dwell on the boundedness of Marcinkiewicz integrals with rough kernel associated with schrodinger operators and commutators generated by these operators and local Campanato functions both on generalized local Morrey spaces and on generalized vanishing local Morrey spaces, respectively. As an application of the above results, the boundedness of parametric Marcinkiewicz integral and its commutator both on generalized local Morrey spaces and on generalized vanishing local Morrey spaces is also obtained.