%0 Journal Article
%T Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
%A J. M. Aldaz
%A J. P¨Śrez L¨˘zaro
%J Mathematics
%D 2006
%I arXiv
%X We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain, under less regularity, versions of classical inequalities involving derivatives.
%U http://arxiv.org/abs/math/0601044v2