Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities

2024/11/13 by Hong Wang, Shukun Wu, Wang, Hong +1 · 10 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2411.08871

openalex publication_date 2024/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose to study the restriction conjecture using decoupling theorems and two-ends Furstenberg inequalities. Specifically, we pose a two-ends Furstenberg conjecture, which implies the restriction conjecture. As evidence, we prove this conjecture in the plane by using the Furstenberg set estimate. Moreover, we use this planar result to prove a restriction estimate for p>22/7 in three dimensions, which implies Wolff's 5/2-hairbrush bound for Kakeya sets in ℝ³. Our approach also makes improvements for the restriction conjecture in higher dimensions.

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