## Acta Mathematica

### On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1

#### 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 L2(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.

#### Article information

Source
Acta Math., Volume 213, Number 2 (2014), 237-321.

Dates
First available in Project Euclid: 30 January 2017

https://projecteuclid.org/euclid.acta/1485801867

Digital Object Identifier
doi:10.1007/s11511-014-0120-7

Mathematical Reviews number (MathSciNet)
MR3286036

Zentralblatt MATH identifier
1311.28004

Rights

#### Citation

Nazarov, Fedor; Volberg, Alexander; Tolsa, Xavier. On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1. Acta Math. 213 (2014), no. 2, 237--321. doi:10.1007/s11511-014-0120-7. https://projecteuclid.org/euclid.acta/1485801867

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