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

摘要

Suppose (L=-Delta+V) is a Schrödinger operator on (mathbb{R}^n), where (ngeq 3) and the nonnegative potential (V) belongs to reverse Hölder class (RH_{n}.) Let (b) belong to a new Campanato space (Lambda_eta^heta(ho),) and let (mu_j^L) be the Marcinkiewicz integrals associated with (L.) In this paper, we establish the boundedness of the (m)-order commutators ([b^m, mu_j^L]) from (L^p(mathbb{R}^n)) to (L^q(mathbb{R}^n),) where (1/q=1/p-meta) and (1pn/(meta).) As an application, we obtain the boundedness of ([b^m, mu_j^L]) on the generalized Morrey spaces related to certain nonnegative potentials.