The One-Third-Trick and Shift Operators

Volume 61 / 2013

Richard Lechner Bulletin Polish Acad. Sci. Math. 61 (2013), 219-238 MSC: Primary 46E40. DOI: 10.4064/ba61-3-4


We obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation.


  • Richard LechnerInstitute of Analysis
    Johannes Kepler University Linz
    Altenbergerstrasse 69
    A-4040 Linz, Austria

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