Work

Construction of a curved Kakeya set

Year: 2025

Type: article

Abstract: We construct a compact set in 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 ‐ norm of the corresponding maximal operator for a range of . Moreover, our construction can be generalised from parabolas to a family of curves satisfying suitable curvature conditions.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70110

Authors: Tongou Yang, Yue Zhong

Institutions: University of California, Los Angeles, Sun Yat-sen University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G2428582065, G7025268907