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Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications

We prove uniform Sobolev estimates for the resolvent of Schrödinger operators with large scaling-critical potentials without any repulsive condition. As applications, global-in-time Strichartz estimates including some non-admissible retarded estimates, a Hörmander type spectral multiplier theorem, and Keller type eigenvalue bounds with complex-valued potentials are also obtained.