Some remarks on Fourier restriction estimates

2017/02/04 by Jongchon Kim, Kim, Jongchon · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.01231

openalex publication_date 2017/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide L^p → L^q refinements on some Fourier restriction estimates obtained using polynomial partitioning. Let S⊂ ℝ³ be a compact C^∞ surface with strictly positive second fundamental form. We derive sharp L^p(S) → L^q(ℝ³) estimates for the associated Fourier extension operator for q> 3.25 and q≥ 2p' from an estimate of Guth that was used to obtain L^∞(S) → L^q(ℝ³) bounds for q>3.25. We present a slightly weaker result when S is the hyperbolic paraboloid in ℝ³ based on the work of Cho and Lee. Finally, we give some refinements for the truncated paraboloid in higher dimensions.

Citations

• On the multilinear restriction and Kakeya conjectures

Cited by

• Restriction estimates for 2D surfaces of finite type 3 and applications to dispersive equations
• A restriction estimate for surfaces with negative Gaussian curvatures

Related

• Fourier restriction estimates for surfaces of co-dimension two in ℝ⁵
• A restriction estimate using polynomial partitioning
• A restriction estimate in ℝ³ using brooms
• L^p-L² Fourier restriction for hypersurfaces in \Bbb R³: Part II
• Fourier restriction for smooth hyperbolic 2-surfaces