Weighted inequalities for negative powers of Schrödinger operators

In this article we obtain boundedness of the operator (− + V )−α/2 from Lp,∞(w) into weighted bounded mean oscillation type spaces BMOβ L(w) under appropriate conditions on the weight w. We also show that these weighted spaces also have a point-wise description for 0<β <1. Finally, we study the behaviour of the operator (− + V )−α/2 when acting on BMOβ L(w).