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

2012/12/20 by Fëdor Nazarov, Xavier Tolsa, Nazarov, Fedor +3 · 5 citations
Mathematics · #35R35 #42B20 #49Q15 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1212.5229

openalex publication_date 2012/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if \μ is a d-dimensional Ahlfors-David regular measure in\n R^d+1, then the boundedness of the d-dimensional Riesz transform in\nL²(\μ) implies that the non-BAUP David-Semmes cells form a Carleson family.\nCombined with earlier results of David and Semmes, this yields the uniform\nrectifiability of \μ.\n

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