Zygmund type and flag type maximal functions, and sparse operators

Guillermo J. Flores, Ji Li, Lesley A. Ward

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)555-567
Number of pages13
JournalProceedings of the American Mathematical Society
Volume151
Issue number2
DOIs
Publication statusPublished - Feb 2023

Keywords

  • maximal functions
  • sparse domination
  • Zygmund dilations

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