Weighted decoupling with lower-dimensional frequency localization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909011675185152 |
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| author | Kim, Jongchon |
| author_facet | Kim, Jongchon |
| contents | We prove weighted $L^2$ and refined $L^p$ decoupling estimates for functions whose Fourier transforms are supported in a small neighborhood of the unit sphere or the truncated paraboloid with an additional lower-dimensional frequency localization property. As a special case, we recover the fractal $L^2$ restriction estimate of Du and Zhang, with a sharper dependence on the density of the weight. We also derive weighted refined decoupling estimates related to the Falconer distance set problem, improving earlier results under the stronger assumption that the underlying weight is $α$-dimensional at every scale. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02246 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted decoupling with lower-dimensional frequency localization Kim, Jongchon Classical Analysis and ODEs Analysis of PDEs 42B15, 42B37 We prove weighted $L^2$ and refined $L^p$ decoupling estimates for functions whose Fourier transforms are supported in a small neighborhood of the unit sphere or the truncated paraboloid with an additional lower-dimensional frequency localization property. As a special case, we recover the fractal $L^2$ restriction estimate of Du and Zhang, with a sharper dependence on the density of the weight. We also derive weighted refined decoupling estimates related to the Falconer distance set problem, improving earlier results under the stronger assumption that the underlying weight is $α$-dimensional at every scale. |
| title | Weighted decoupling with lower-dimensional frequency localization |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B15, 42B37 |
| url | https://arxiv.org/abs/2605.02246 |