Adjacent dyadic systems and the $L^p$-boundedness of shift operators in metric spaces revisited

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.