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

Olli Tapiola — 2016

Colloquium Mathematicae

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

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

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