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Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications (1609.03253v6)
Published 12 Sep 2016 in math.AP
Abstract: 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.