The One-Third-Trick and Shift Operators
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 219-238
MSC: Primary 46E40.
DOI: 10.4064/ba61-3-4
Abstract
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.
