{c}
{title2=$Mf$}
{wiki=Hardy–Littlewood_maximal_function}

The centered Hardy-Littlewood maximal function on the real line is
$$
Mf(x)=\sup_{r>0}\frac1{2r}\int_{x-r}^{x+r}|f(t)|\,dt.
$$


Hardy-Littlewood maximal function

{wiki=Hardy–Littlewood_maximal_function}

The Hardy–Littlewood maximal function is a fundamental concept in the field of harmonic analysis and functional analysis. It provides a way to associate a function with a maximal operator that is useful in various contexts, particularly in the study of functions and their properties related to integration and approximation.


 Hardy–Littlewood maximal function

ID: hardy-littlewood-maximal-function