Boundedness of high order commutators of Marcinkiewicz integrals associated with Schrodinger operators

Suppose L = -Delta + V is a Schrodinger operator on R-n, where n >= 3 and the nonnegative potential V belongs to reverse Holder class RHn. Let b belong to a new Campanato space Lambda(theta)(beta)(rho), and let mu(L)(j) be the Marcinkiewicz integrals associated with L. In this paper, we establish the boundedness of the m-order commutators [b(m), mu(L)(j)] from L-p(R-n) to L-q(R-n), where 1/q = 1/p - m beta/n and 1 < p < n = (m beta). As an application, we obtain the boundedness of [b(m), mu(L)(j)] on the generalized Morrey spaces related to certain nonnegative potentials. (C) 2017 All rights reserved.