Riesz transforms and the BAUPP and BWGL criteria for uniform rectifiability

2025/09/30 by Tolsa, Xavier
#28A75 #42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.26547

Abstract

In this note it is shown that if μ is an n-Ahlfors regular measure in \mathbb Rⁿ⁺¹ such that the n-dimensional Riesz transform is bounded in L²(μ) and the so-called BAUPP (bilateral approximation by unions of parallel planes) condition holds for μ, then μ satisfies the BWGL (bilateral weak geometric lemma), and so μ is uniformly n-rectifiable. In this way, one can solve the David-Semmes problem in codimension one without relying on the BAUP (bilateral approximation by unions of planes) criterion of David and Semmes.

Citations

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

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