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

Abstract

Suppose L = −∆ + V is a Schrödinger operator on R n , where n 3 and the nonnegative potential V belongs to reverse Hölder class RH n . Let b belong to a new Campanato space Λ θ β (ρ), and let µ L j be the Marcinkiewicz integrals associated with L. In this paper, we establish the boundedness of the m-order, where 1/q = 1/p − mβ/n and 1 < p < n/(mβ). As an application, we obtain the boundedness of [b m , µ L j ] on the generalized Morrey spaces related to certain nonnegative potentials.