Geodesic
The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension
J. M. Aldaz1
1 Universidad Autonoma de Madrid<br/> Ciudad Universitaria de Cantoblanco 28049 Madrid<br/> Spain
Annals of mathematics, Tome 173 (2011) no. 2, pp. 1013-1023.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 longstanding open question of E. M. Stein and J. O. Strömberg.
DOI : 10.4007/annals.2011.173.2.10

J. M. Aldaz 1

1 Universidad Autonoma de Madrid<br/> Ciudad Universitaria de Cantoblanco 28049 Madrid<br/> Spain 
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J. M. Aldaz. The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension. Annals of mathematics, Tome 173 (2011) no. 2, pp. 1013-1023. doi : 10.4007/annals.2011.173.2.10. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.2.10/

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