Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
J. M. Aldaz, J. Pérez Lázaro
Abstract
We prove that if f:I⊂ R R is of bounded variation, then the noncentered maximal function Mf is absolutely continuous, and its derivative satisfies the sharp inequality \|DMf\|1 |Df|(I). This allows us obtain, under less regularity, versions of classical inequalities involving derivatives.
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