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

Volume 145 / 2016

Olli Tapiola Colloquium Mathematicum 145 (2016), 121-135 MSC: Primary 30L99; Secondary 46E40. DOI: 10.4064/cm6594-11-2015 Published online: 2 May 2016

Abstract

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 \lt p \lt \infty $, $X$ is a metric space and $E$ is a UMD space.

Authors

  • Olli TapiolaDepartment of Mathematics and Statistics
    P.O. Box 68 (Gustaf Hällströmin katu 2b)
    FI-00014 University of Helsinki, Finland
    e-mail

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