Sharp estimates of the Schr\"{o}dinger type propagators on modulation spaces
Abstract
This paper is devoted to conducting a comprehensive and self-contained study of the boundedness on modulation spaces of Fourier integral operators arising when solving Schr\"{o}dinger type operators. The symbols of these operators belong to the Sj\"{o}strand class , and their phase functions satisfy certain regularity conditions associated with mixed modulation spaces. Our conclusions cover two novel situations corresponding to the so-called mild and high growth of phase functions. These conclusions represent essential improvements and generalizations of existing results. Our method is based on a reasonable decomposition and scaling of the symbol and phase functions, ensuring their membership in appropriate mixed modulation spaces. In a certain sense, all conclusions of this paper are optimal.
Cite
@article{arxiv.2507.05039,
title = {Sharp estimates of the Schr\"{o}dinger type propagators on modulation spaces},
author = {Weichao Guo and Guoping Zhao},
journal= {arXiv preprint arXiv:2507.05039},
year = {2025}
}