An Approach To Endpoint Problems in Oscillatory Singular Integrals

2025/02/26 by Alex Iosevich, Ben Krause, Iosevich, Alex +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2502.19302

openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from L¹(ℝ) to L^1,∞(ℝ). The methods we use are entirely elementary, and rely only on pigeonholing and stationary phase considerations.

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