On weighted Compactness of Commutator of semi-group maximal function associated to Schrödinger operators

Abstract

Let T * be the semi-group maximal function associated to the Schrödinger operator −∆ +V (x) with V satisfying an appropriate reverse Hölder inequality. In this paper, we show that the commutator of T * is a compact operator on L p (w)The space where b belongs and the weighs class w belongs are more larger than the usual CMO(R n ) space and the Muckenhoupt A p weights class, respectively.