**Loukas Grafakos and Stephen Montgomery-Smith, Best constants for uncentered maximal functions.**
*Bul. London Math. Soc., ***29**, (1997), 60-64.
We precisely evaluate the operator norm of the uncentered Hardy-Littlewood maximal function on \(L^p(\mathbb R^1)\), showing that it is the unique positive root of the polynomial \((p-1)x^p-px^{p-1}-1\). Consequently, we compute the operator norm of the "strong" maximal function on \(L^p(\mathbb R^n)\), and we observe that the operator norm of the uncentered Hardy-Littlewood maximal function over balls on \(L^p(\mathbb R^n)\) grows exponentially as \(n\to\infty\).
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