  We show that Petermichl's dyadic operator $\mathcal{P}$ (S. Petermichl
(2000), Dyadic shifts and a logarithmic estimate for Hankel operators with
matrix symbol) is a Calder\'{o}n-Zygmund type operator on an adequate metric
normal space of homogeneous type. As a consequence of a general result on
spaces of homogeneous type, we get weighted boundedness of the maximal operator
$\mathcal{P}^*$ of truncations of the singular integral. We show that dyadic
$A_p$ weights are the good weights for the maximal operator $\mathcal{P}^*$ of
the scale truncations of $\mathcal{P}$.
