Maximal estimates for averages over degenerate hypersurfaces

2025/01/01 by Sekyung Oh, Oh, Sewook
Mathematics · #42B20 #42B25 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2501.00858

openalex publication_date 2025/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study L^p boundedness of the maximal average over dilations of a smooth hypersurface S. When the decay rate of the Fourier transform of a measure on S is 1/2, we establish the optimal maximal bound, which settles the conjecture raised by Stein. Additionally, when S is not flat, we verify that the maximal average is bounded on L^p for some finite p, which generalizes the result by Sogge and Stein.

Related

• Maximal averages over hypersurfaces and the Newton polyhedron
• Maximal averages associated to families of finite type surfaces
• L^p boundedness of maximal averages over hypersurfaces in R³
• Estimates for maximal functions associated to hypersurfaces in \Bbb R³ with height h<2: Part I
• Smooth and singular maximal averages over 2D hypersurfaces and\n associated Radon transforms