Uniform Sobolev estimates for Schr\"odinger operators with   scaling-critical potentials and applications
  We prove uniform Sobolev estimates for the resolvent of Schr\"odinger operators with large scaling-critical potentials without any repulsive condition. As applications, global-in-time Strichartz estimates including some non-admissible retarded estimates, a H\"ormander type spectral multiplier theorem, and Keller type eigenvalue bounds with complex-valued potentials are also obtained. 
Haruya Mizutani
math.AP