Sparse domination and the strong maximal function

2018/11/03 by Barron, Alex, Conde-Alonso, Jose M., Ou, Yumeng +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.01243

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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