Functions of Bounded Variation, the Derivative of the One Dimensional Maximal Function, and Applications to Inequalities
نویسندگان
چکیده
We prove that if f : I ⊂ R → R is of bounded variation, then the uncentered maximal function Mf is absolutely continuous, and its derivative satisfies the sharp inequality ‖DMf‖L1(I) ≤ |Df |(I). This allows us obtain, under less regularity, versions of classical inequalities involving derivatives.
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تاریخ انتشار 2006