On the Variation of the Hardy–littlewood Maximal Function
نویسنده
چکیده
We show that a function f : R → R of bounded variation satisfies VarMf ≤ C Var f, where Mf is the centered Hardy–Littlewood maximal function of f . Consequently, the operator f 7→ (Mf) is bounded from W (R) to L(R). This answers a question of Hajłasz and Onninen in the one-dimensional case.
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