Let $\mu$ be the Hardy Littlewood centered maximal operator in $\mathbb{R}^n$
$\mu (f)(x) = \sup_{r>0} \frac{1}{|B_r(x)|} \int_{B_r(x)} |f(y)|dy.$
If $g(x)=|x|^{-\eta}$, com $\eta \in (0,n)$, how to prove that $\mu(g)(x)=Cg(x)$, for some $C$ constant?