Sparse domination and the strong maximal function

Alex Barron; José M. Conde-Alonso; Yumeng Ou; Guillermo Rey

doi:10.1016/j.aim.2019.01.007

Sparse domination and the strong maximal function

Alex Barron
, José M. Conde-Alonso
, Yumeng Ou
, Guillermo Rey

School of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We study the problem of dominating the dyadic strong maximal function by (1,1)-type sparse forms based on rectangles with sides parallel to the axes, and show that such domination is impossible. Our proof relies on an explicit construction of a pair of maximally separated point sets with respect to an appropriately defined notion of distance.

Original language	English (US)
Pages (from-to)	1-26
Number of pages	26
Journal	Advances in Mathematics
Volume	345
DOIs	https://doi.org/10.1016/j.aim.2019.01.007
State	Published - Mar 17 2019

Bibliographical note

Funding Information:
The authors would like to thank Jill Pipher and Dmitriy Bilyk for useful discussions regarding the content of this paper. The third named author is supported by NSF-DMS #1764454.

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Biparameter
Maximal functions
Multiparameter
Sparse domination

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10.1016/j.aim.2019.01.007

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abstract = "We study the problem of dominating the dyadic strong maximal function by (1,1)-type sparse forms based on rectangles with sides parallel to the axes, and show that such domination is impossible. Our proof relies on an explicit construction of a pair of maximally separated point sets with respect to an appropriately defined notion of distance.",

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author = "Alex Barron and Conde-Alonso, \{Jos{\'e} M.\} and Yumeng Ou and Guillermo Rey",

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AU - Ou, Yumeng

AU - Rey, Guillermo

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AB - We study the problem of dominating the dyadic strong maximal function by (1,1)-type sparse forms based on rectangles with sides parallel to the axes, and show that such domination is impossible. Our proof relies on an explicit construction of a pair of maximally separated point sets with respect to an appropriately defined notion of distance.

KW - Biparameter

KW - Maximal functions

KW - Multiparameter

KW - Sparse domination

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JO - Advances in Mathematics

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ER -

Sparse domination and the strong maximal function

Abstract

Bibliographical note

Keywords

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