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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07934 |
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| _version_ | 1866910046103797760 |
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| author | Kim, Jongchon Wang, Liang Yeung, Chun Keung |
| author_facet | Kim, Jongchon Wang, Liang Yeung, Chun Keung |
| contents | In this paper, we prove small cap square function and decoupling estimates for the parabola, where the small caps are essentially axis-parallel rectangles of dimensions $δ\times δ^β$ for $0\leq β\leq 1$. Our estimates complement the known results for $1 \leq β\leq 2$ and are sharp up to polylogarithmic factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07934 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on small cap square function and decoupling estimates for the parabola Kim, Jongchon Wang, Liang Yeung, Chun Keung Classical Analysis and ODEs In this paper, we prove small cap square function and decoupling estimates for the parabola, where the small caps are essentially axis-parallel rectangles of dimensions $δ\times δ^β$ for $0\leq β\leq 1$. Our estimates complement the known results for $1 \leq β\leq 2$ and are sharp up to polylogarithmic factors. |
| title | A note on small cap square function and decoupling estimates for the parabola |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.07934 |