Sharp estimates of the Schrödinger type propagators on modulation spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912468917288960 |
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| author | Guo, Weichao Zhao, Guoping |
| author_facet | Guo, Weichao Zhao, Guoping |
| contents | 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 Schrödinger type operators. The symbols of these operators belong to the Sjöstrand 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp estimates of the Schrödinger type propagators on modulation spaces Guo, Weichao Zhao, Guoping Classical Analysis and ODEs 35S30, 47G30, 42B35 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 Schrödinger type operators. The symbols of these operators belong to the Sjöstrand 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. |
| title | Sharp estimates of the Schrödinger type propagators on modulation spaces |
| topic | Classical Analysis and ODEs 35S30, 47G30, 42B35 |
| url | https://arxiv.org/abs/2507.05039 |