L^p weighted Fourier restriction estimates

2024/04/16 by Xiumin Du, Du, Xiumin, Jianhui Li +5
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.10951

openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain some sharp L^p weighted Fourier restriction estimates of the form ‖Ef‖_{L^p(Bⁿ⁺¹(0,R),Hdx)} \lessapprox R^β‖f‖₂, where E is the Fourier extension operator over the truncated paraboloid, and H is a weight function on \mathbb Rⁿ⁺¹ which is n-dimensional up to scale √ R.

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