The one-dimensional centred maximal function diminishes the variation of indicator functions

2021/07/26 by Constantin Bilz, Bilz, Constantin, Julian Weigt +1
Computer Science · Mathematics · #42B25 (Primary) 26A45 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.12404

openalex publication_date 2021/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results to a larger class of functions.

Citations

• On regularity of the discrete Hardy-Littlewood maximal function

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