On the Haar Shift representations of Calderón-Zygmund Operators

Abstract

In connection with proving the A_2 conjecture in 2010, T. Hytönen obtained a representation of general Caldéron-Zygmund operators in terms of simpler operators known as Haar shifts. In this note, we prove that the result is sharp in the sense that Haar shift representations of Hytönen's type are only available for Calderón-Zygmund operators.

7 pages. v2: typos corrected, to appear in Proc. AMS