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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 language | English |
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Pages (from-to) | 555-567 |
Number of pages | 13 |
Journal | Proceedings of the American Mathematical Society |
Volume | 151 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2023 |
Keywords
- maximal functions
- sparse domination
- Zygmund dilations
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Dive into the research topics of 'Zygmund type and flag type maximal functions, and sparse operators'. Together they form a unique fingerprint.Projects
- 1 Finished
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Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals
Duong, X., Ward, L., Li, J., Lacey, M., Pipher, J. & MQRES, M.
16/02/16 → 30/06/20
Project: Research