L^p boundedness of maximal averages over hypersurfaces in R³

2010/08/23 by Michael Greenblatt, Greenblatt, Michael
Mathematics · #42B20 42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1008.3931

openalex publication_date 2010/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Extending the methods developed in the author's previous paper and using adapted coordinate systems in two variables, an L^p boundedness theorem is proven for maximal operators over hypersurfaces in R³ when p > 2. When the best possible p is greater than 2, the theorem typically provides sharp estimates. This gives another approach to the subject of recent work of Ikromov, Kempe, and Muller on this subject

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