  With the help of recent adjacent dyadic constructions by Hyt\"onen and the
author, we give an alternative proof of results of Lechner, M\"uller and
Passenbrunner about the $L^p$-boundedness of shift operators acting on
functions $f \in L^p(X;E)$ where $1 < p < \infty$, $X$ is a metric space and
$E$ is a UMD space.
