Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality

In this paper we study some questions in connection with uniform rectifiability and the L2 boundedness of Calderón-Zygmund operators (CZOs). We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients that are related to the Jones' β numbers. We also use these new coefficients to prove that n-dimensional CZOs with odd kernel of type script C sign2 are bounded in L 2(μ), if μ is an n-dimensional uniformly rectifiable measure. © 2008 London Mathematical Society.