Uniform Sobolev estimates for Schr\"odinger operators with scaling-critical potentials and applications
Analysis of PDEs
2020-07-29 v6
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.
Keywords
Cite
@article{arxiv.1609.03253,
title = {Uniform Sobolev estimates for Schr\"odinger operators with scaling-critical potentials and applications},
author = {Haruya Mizutani},
journal= {arXiv preprint arXiv:1609.03253},
year = {2020}
}
Comments
31 pages, 1 figure; revised version