Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities

Details Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities

2006-01-03

arxiv.org/abs/math/0601044v2

Trans. Amer. Math. Soc. 359 (2007), no. 5, 2443--2461

Mathematics

Classical Analysis and ODEs

To appear, TAMS, 21 pages

Scientific paper

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.

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