A remark on the Hardy-Littlewood maximal functions

2022/11/06 by Wu-yi Pan, Pan, Wu-yi
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2211.03121

openalex publication_date 2022/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the magnitude relation of the non-centered Hardy-Littlewood maximal operators and centered one. By using a discretization technique, we prove two facts: the first one is that the space is ultrametric if and only if the two maximal operators are identical for all discrete measure; the second is, the uncentred maximal operator is strictly greater than the centered one if (M,d_g) is a Riemannian manifold and μ is the Riemannian volume measure.

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