Maximal averages along a planar vector field depending on one variable

2011/04/14 by Michael Bateman, Bateman, Michael
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary: 42B25 Secondary: 42B20 #math.CA #msc:42B20 #msc:42B25

paper · pdf · doi:10.48550/arxiv.1104.2859

20 pages

arxiv created 2011/04/14 · openalex publication_date 2011/04/14 · arxiv updated 2011/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove (essentially) sharp L² estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines an understanding of such vector fields from earlier work of the author with a result of Nets Katz on directional maximal operators.

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