On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
By Fedor Nazarov, Alexander Volberg, Xavier Tolsa. 2012
160 citations recorded by the source corpus.
We prove that if μ is a d-dimensional Ahlfors-David regular measure in $${\mathbb{R}^{d+1}}$$Rd+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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d060d3f97c47815801550ffde3a61306f9c6d8a9
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In Applied Mathematics
- Xavier Tolsa
- Tuomas Hytönen
- Dachun Yang
- Wen Yuan
- Xing Fu
- Yoshihiro Sawano
- Hitoshi Tanaka
- Dongyong Yang
In Mathematical Physics
- Xavier Tolsa
- Tuomas Hytönen
- Dachun Yang
- Wen Yuan
- Xing Fu
- Yoshihiro Sawano
- Hitoshi Tanaka
- Alexander Volberg
Citations in the corpus
- Characterization of n-rectifiability in terms of Jones’ square function: part I (2015, background): “More recently, the development of quantitative rectifiability in the pioneering works of Jones [10] and David and Semmes [8] has led to the study of the connection between rectifiability and the boundedness of square functions and singular integrals (for instance, see [6,7,11,15]).”