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math.CA2025
New criteria for the rectifiability of Radon measures in terms of Riesz transforms
Xavier Tolsa
In this paper we explore the connection between quantitative rectifiability of measures and the boundedness of the codimension one Riesz transform. Among other things, we pro…
math.CA2025
Riesz transforms and the BAUPP and BWGL criteria for uniform rectifiability
Xavier Tolsa
In this note it is shown that if is an -Ahlfors regular measure in such that the -dimensional Riesz transform is bounded in and the so-called B…
math.CA2025
Quantitative Carleson's conjecture for Ahlfors regular domains
Emily Casey, Xavier Tolsa, Michele Villa
In this article, we prove a quantitative version of Carleson's conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n…