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arXiv · 2507.05039

Sharp estimates of the Schr\"{o}dinger type propagators on modulation spaces

Weichao Guo·Guoping Zhao
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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 $M^{\infty,1}$, 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.

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Weichao Guo, Guoping Zhao. 2025-07-07. Sharp estimates of the Schr\"{o}dinger type propagators on modulation spaces. https://arxiv.org/abs/2507.05039

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