Maximal Functions for Lacunary Dilation Structures

2012/10/27 by Patrick LaVictoire, LaVictoire, Patrick
Mathematics · #42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.CA #msc:42B25

paper · pdf · doi:10.48550/arxiv.1210.7379

12 pages, LaTeX

arxiv created 2012/10/27 · openalex publication_date 2012/10/27 · arxiv updated 2012/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If mu is a smooth density on a hypersurface in R^d whose curvature never vanishes to infinite order, and A is a d-by-d matrix whose eigenvalues all have absolute value greater than 1, then the maximal function given by convolving f with dilates of mu by powers of A, and taking the maximum, is bounded from a corresponding version of H¹ to weak L¹.

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