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arXiv · 0805.1565

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

J. M. Aldaz
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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 long standing open question of E. M. Stein and J. O. Strömberg.

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J. M. Aldaz. 2010-09-06. The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension. https://arxiv.org/abs/0805.1565

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