Abstract
We prove that if μ is a d-dimensional Ahlfors-David regular measure in \({\mathbb{R}^{d+1}}\) , then the boundedness of the d-dimensional Riesz transform in L 2(μ) implies that the non-BAUP David–Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of μ.
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Nazarov, F., Volberg, A. & Tolsa, X. On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1. Acta Math 213, 237–321 (2014). https://doi.org/10.1007/s11511-014-0120-7
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DOI: https://doi.org/10.1007/s11511-014-0120-7