Construction of a curved Kakeya set

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-05-30 DOI:10.1112/blms.70110

Tongou Yang, Yue Zhong

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引用次数: 0

Abstract

We construct a compact set in $R^{2}$ 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.