Charles Explorer logo
🇬🇧

ON THE VARIATION OF THE HARDY-LITTLEWOOD MAXIMAL FUNCTION

Publication at Faculty of Mathematics and Physics |
2015

Abstract

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.