Zygmund type and flag type maximal functions, and sparse operators

2020/02/18 by Guillermo Flores, Ji Li, Flores, Guillermo J. +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2002.07616

openalex publication_date 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the maximal functions associated with a Zygmund dilation dyadic structure in three-dimensional Euclidean space, and with the flag dyadic structure in two-dimensional Euclidean space, cannot be bounded by multiparameter sparse operators associated with the corresponding dyadic grid. We also obtain supplementary results about the absence of sparse domination for the strong dyadic maximal function.

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