Fourier extension estimates on a strip in ℝ²

2025/08/28 by Bulj, Aleksandar, Shiraki, Shobu
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.20463

Abstract

Given a smooth curve with nonzero curvature Σ⊂ ℝ², let E_Σ denote the associated Fourier extension operator. For both general compact curves and the parabola, we characterize the pairs (p,q)∈ [1,∞]² for which the estimates ‖E_Σf‖_L^q(Ω)≤ C‖f‖_L^p(Σ) and (R(|E_Σf|^q))^(1)/(q)≤ C‖f‖_L^p(Σ) hold, where Ω is a strip in ℝ² and R denotes the Radon transform. This work continues the study of mass concentration of x↦ E_Σf(x) near lines in ℝ², initiated by Bennett and Nakamura and later extended by Bennett, Nakamura, and the second author, where expressions of the form (R(|E_Σf|²))^(1)/(2) were studied.

Citations

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