Construction of a curved Kakeya set
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866918013409689600 |
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| author | Yang, Tongou Zhong, Yue |
| author_facet | Yang, Tongou Zhong, Yue |
| contents | We construct a compact set in $\mathbb R^2$ of measure 0 containing a piece of a parabola of every aperture between 1 and 2. As a consequence, we improve lower bounds for the $L^p$-$L^q$ norm of the corresponding maximal operator for a range of $p$, $q$. Moreover, our construction can be generalised from parabolas to a family of $C^2$ curves satisfying suitable curvature conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of a curved Kakeya set Yang, Tongou Zhong, Yue Classical Analysis and ODEs 42B99 We construct a compact set in $\mathbb R^2$ of measure 0 containing a piece of a parabola of every aperture between 1 and 2. As a consequence, we improve lower bounds for the $L^p$-$L^q$ norm of the corresponding maximal operator for a range of $p$, $q$. Moreover, our construction can be generalised from parabolas to a family of $C^2$ curves satisfying suitable curvature conditions. |
| title | Construction of a curved Kakeya set |
| topic | Classical Analysis and ODEs 42B99 |
| url | https://arxiv.org/abs/2408.01917 |