The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension

Details The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension

2008-05-11

arxiv.org/abs/0805.1565v5

Ann. of Math. (2) 173 (2011), no. 2, 1013-1023

Mathematics

Classical Analysis and ODEs

A very similar version to this posting (but with fewer explicit constants, in order to satisfy the requests of an anonymous re

Scientific paper

Let $M_d$ be the centered Hardy-Littlewood maximal function associated to
cubes in $\mathbb{R}^d$ with Lebesgue measure, and let $c_d$ denote the lowest
constant appearing in the weak type (1,1) inequality satisfied by $M_d$.
We show that $c_d \to \infty$ as $d\to \infty$, thus answering, for the case
of cubes, a long standing open question of E. M. Stein and J. O. Str\"{o}mberg.

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