Riesz transforms and Littlewood–Paley square function associated to schrödinger operators on new weighted spaces

Abstract

Let Delta L=−Delta+V be a Schrödinger operator on Rn,n≥3 , where V is a potential satisfying an appropriate reverse Hölder inequality. In this paper, we prove the boundedness of the Riesz transforms and the Littlewood–Paley square function associated with Schrödinger operators L in some new function spaces, such as new weighted Bounded Mean Oscillation (BMO) and weighted Lipschitz spaces, associated with L . Our results extend certain well-known results.