Near Optimal L^p→ L^q Estimates for Euclidean Averages Over Prototypical Hypersurfaces in ℝ³

2020/12/31 by Jeremy Schwend, Schwend, Jeremy
Mathematics · #42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2012.15789

openalex publication_date 2020/12/31 · openalex created_date 2024/01/04 · openalex updated_date 2026/08/01

Abstract

We find the precise range of (p,q) for which local averages along graphs of a class of two-variable polynomials in ℝ³ are of restricted weak type (p,q), given the hypersurfaces have Euclidean surface measure. We derive these results using non-oscillatory, geometric methods, for a model class of polynomials bearing a strong connection to the general real-analytic case.

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