ON THE VARIATION OF THE HARDY-LITTLEWOOD MAXIMAL FUNCTION

Abstrakt

We show that a function f of bounded variation satisfies that Var(Mf) is less than or equal to C Var(f) for some absolute constant C, where Mf is the centered Hardy-Littlewood maximal function of f. This allows us to answer a question of Hajlasz and Onninen in the one-dimensional case.

Klíčová slova

• Hardy-Littlewood maximal function
• function of bounded variation
• weak differentiability