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2020 Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications
Haruya Mizutani
Anal. PDE 13(5): 1333-1369 (2020). DOI: 10.2140/apde.2020.13.1333

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 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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Haruya Mizutani. "Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications." Anal. PDE 13 (5) 1333 - 1369, 2020. https://doi.org/10.2140/apde.2020.13.1333

Information

Received: 23 October 2017; Revised: 22 September 2018; Accepted: 31 May 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07271832
MathSciNet: MR4149064
Digital Object Identifier: 10.2140/apde.2020.13.1333

Subjects:
Primary: 35J10 , 35P25
Secondary: 35P15 , 35Q41

Keywords: eigenvalue bounds , limiting absorption principle , Schrödinger equation , spectral multiplier theorem , Strichartz estimate , uniform Sobolev estimate

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 5 • 2020
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