Spectral Multipliers for Schroedinger Operators

Abstract: 

We consider Hormander type spectral multiplier problem for Schroedinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on Lp, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations.

Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.