Local smoothing estimates for Schrödinger equations in modulation spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918152677359616 |
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| author | Inami, Kotaro |
| author_facet | Inami, Kotaro |
| contents | Motivated by a recent work of Schippa (2022), we consider local smoothing estimates for Schrödinger equations in modulation spaces. By using the Córdoba-Fefferman type reverse square function inequality and the bilinear Strichartz estimate, we can refine the summability exponent of modulation spaces. Next, we will also discuss a new type of randomized Strichartz estimate in modulation spaces. Finally, we will show that the reverse function estimate implies the Strichartz estimates in modulation spaces. From this implication, we obtain the reverse square function estimate of critical order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local smoothing estimates for Schrödinger equations in modulation spaces Inami, Kotaro Classical Analysis and ODEs Motivated by a recent work of Schippa (2022), we consider local smoothing estimates for Schrödinger equations in modulation spaces. By using the Córdoba-Fefferman type reverse square function inequality and the bilinear Strichartz estimate, we can refine the summability exponent of modulation spaces. Next, we will also discuss a new type of randomized Strichartz estimate in modulation spaces. Finally, we will show that the reverse function estimate implies the Strichartz estimates in modulation spaces. From this implication, we obtain the reverse square function estimate of critical order. |
| title | Local smoothing estimates for Schrödinger equations in modulation spaces |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2412.18363 |