Geodesic
A remark on the centered $n$-dimensional Hardy-Littlewood maximal function
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 103-112.

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We study the behaviour of the $n$-dimensional centered Hardy-Littlewood maximal operator associated to the family of cubes with sides parallel to the axes, improving the previously known lower bounds for the best constants $c_n$ that appear in the weak type $(1,1)$ inequalities.
Classification : 42A99, 42B25
Keywords: Hardy-Littlewood maximal function 
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     title = {A remark on the centered $n$-dimensional {Hardy-Littlewood} maximal function},
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Aldaz, J. M. A remark on the centered $n$-dimensional Hardy-Littlewood maximal function. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 103-112. http://geodesic.mathdoc.fr/item/CMJ_2000__50_1_a13/