Weighted wave envelope estimates for the parabola
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915687906148352 |
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| author | Kim, Jongchon Ko, Hyerim |
| author_facet | Kim, Jongchon Ko, Hyerim |
| contents | In this paper, we extend the Córdoba-Fefferman square function estimate for the parabola to a weighted setting. Our weighted square function estimate is derived from a weighted wave envelope estimate for the parabola. The bounds are formulated in terms of families of multiscale tubes together with weight parameters that quantify the distribution of the weight. As an application, we obtain some weighted L^p-estimates for a class of Fourier multiplier operators and for solutions to free Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted wave envelope estimates for the parabola Kim, Jongchon Ko, Hyerim Classical Analysis and ODEs Analysis of PDEs 42B15, 42B25 In this paper, we extend the Córdoba-Fefferman square function estimate for the parabola to a weighted setting. Our weighted square function estimate is derived from a weighted wave envelope estimate for the parabola. The bounds are formulated in terms of families of multiscale tubes together with weight parameters that quantify the distribution of the weight. As an application, we obtain some weighted L^p-estimates for a class of Fourier multiplier operators and for solutions to free Schrödinger equation. |
| title | Weighted wave envelope estimates for the parabola |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B15, 42B25 |
| url | https://arxiv.org/abs/2511.04503 |