Abstract
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.
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author={Aldaz, J. M. and Colzani, L. and Pérez Lázaro, J.},
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