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

J. M. Aldaz·J. Pérez Lázaro
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Abstract

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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BibTeXRIS

J. M. Aldaz, J. Pérez Lázaro. 2006-01-03. Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities. https://arxiv.org/abs/math/0601044

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