建造一套弧形笕屋

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-04 DOI:arxiv-2408.01917

Tongou Yang, Yue Zhong

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引用次数: 0

摘要

我们在 R2 中构造了一个度量为 0 的紧凑集合，其中包含 1 和 2 之间每个孔径的一段抛物线。因此，我们改进了$p$, $q$范围内相应最大算子的$L^p$-$L^q$规范的下限。此外，我们的构造可以从抛物线推广到具有电影曲率的曲线族。

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Construction of a curved Kakeya set

We construct a compact set in R2 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 curves with cinematic curvature.

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arXiv - MATH - Classical Analysis and ODEs

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