The One-Third-Trick and Shift Operators

Abstract

In this paper 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.

References in corpus (2)

• A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type
• Foundations of vector-valued singular integrals revisited---with random dyadic cubes

Cited by in corpus (2)

• Two weight norm inequalities for fractional integral operators and commutators
• Adaptive deterministic dyadic grids on spaces of homogeneous type