We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, thenthe noncentered maximal function $Mf$ is absolutely continuous, and itsderivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allowsus obtain, under less regularity, versions of classical inequalities involvingderivatives.
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机译：我们证明如果$ f：I \ subset \ Bbb R \ to \ Bbb R $是有界变化，那么无心最大值函数$ Mf $是绝对连续的，并且其导数满足尖锐的不等式$ \ | DMf \ | _1 \ le | Df |（I）$。这使我们能够以较少的规律性获得涉及导数的经典不等式的版本。
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