On Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators

Abstract

Let \({\cal L} = - \Delta + V\) be a Schrödinger operator with a nonnegative potential V belonging to the reverse Hölder class B_q for q> n/2. In this paper, we study the weighted compactness of oscillation and variation commutators generated by BMO-type functions and some Schrödinger operators, which include Riesz transform and other standard Calderón–Zygmund operators.