$L^p$-boundedness of shift operators in metric spaces revisited

Olli Tapiola

Published 2015-04-07Version 1

With the help of recent adjacent dyadic constructions by Hyt\"onen and the author, we give a simple alternative proof of results of Lechner 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.