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In this paper we study some questions in connection with uniform rectifiability and the  L  2  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  2  are bounded in  L  2 (μ), if μ is an  n ‐dimensional uniformly rectifiable measure.

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