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Uniform Sobolev
estimates for Schrödinger operators with scaling-critical
potentials and applications
Haruya Mizutani |
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Vol. 13 (2020), No. 5, 1333–1369
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Abstract |
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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 nonadmissible retarded estimates, a Hörmander-type spectral multiplier theorem, and Keller-type eigenvalue bounds with complex-valued potentials are also obtained. |
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Keywords
uniform Sobolev estimate, limiting absorption principle,
Strichartz estimate, spectral multiplier theorem,
eigenvalue bounds, Schrödinger equation
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Mathematical Subject Classification 2010
Primary: 35P25, 35J10
Secondary: 35P15, 35Q41
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Milestones
Received: 23 October 2017
Revised: 22 September 2018
Accepted: 31 May 2019
Published: 27 July 2020
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Authors |
| Haruya Mizutani | |
| Department of Mathematics Graduate School of Science Osaka University Osaka Japan |
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