  We precisely evaluate the operator norm of the uncentered Hardy-Littlewood
maximal function on $L^p(\Bbb R^1)$. We also compute the operator norm of the
uncentered Hardy-Littlewood maximal function over rectangles on $L^p(\Bbb
R^n)$, and we show that the operator norm of the uncentered Hardy-Littlewood
maximal function over balls on $L^p(\Bbb R^n)$ grows exponentially with the
dimension as $n \to \infty$.
