Weighted norm inequalities for oscillatory integrals with finite type phases on the line

2011/10/27 by Jonathan Bennett, Bennett, Jonathan, Samuel Harrison +2
Mathematics · #42B25 #44B20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CA #msc:42B25 #msc:44B20

paper · pdf · doi:10.48550/arxiv.1110.6031

22 pages

arxiv created 2011/10/27 · openalex publication_date 2011/10/27 · arxiv updated 2011/10/28 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We obtain two-weighted L² norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type. The conditions imposed on the weights involve geometrically-defined maximal functions, and the inequalities are best-possible in the sense that they imply the full L^p(ℝ)→ L^q(ℝ) mapping properties of the oscillatory integrals. Our results build on work of Carbery, Soria, Vargas and the first author.

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