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

Mizutani, Haruya

doi:10.2140/apde.2020.13.1333

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

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

Haruya Mizutani

Vol. 13 (2020), No. 5, 1333–1369

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 35P25, 35J10

Secondary: 35P15, 35Q41

Milestones

Received: 23 October 2017

Revised: 22 September 2018

Accepted: 31 May 2019

Published: 27 July 2020

Authors

Haruya Mizutani
Department of Mathematics Graduate School of Science Osaka University Osaka Japan

Vol. 13, No. 5, 2020