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

Abstract

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.

31 pages, 1 figure; revised version

References in corpus (1)

• Kato smoothing and Strichartz estimates for wave equations with magnetic potentials

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• Limiting absorption principle on $L^p$-spaces and scattering theory