A global space-time estimate for dispersive operators through its local estimate
Analysis of PDEs
2021-09-02 v1 Classical Analysis and ODEs
Abstract
We will show that a local space-time estimate implies a global space-time estimate for dispersive operators. In order for this implication we consider a Littlewood-Paley type square function estimate for dispersive operators in a time variable and a generalization of Tao's epsilon removal lemma in mixed norms. By applying this implication to the fractional Schrodinger equation in R^{2+1} we obtain the sharp global space-time estimates with optimal regularity from the previous known local ones.
Cite
@article{arxiv.2109.00382,
title = {A global space-time estimate for dispersive operators through its local estimate},
author = {Chu-hee Cho and Youngwoo Koh and Jungjin Lee},
journal= {arXiv preprint arXiv:2109.00382},
year = {2021}
}
Comments
11 pages, 1 figure