Rectifiable measures, square functions involving densities, and the Cauchy transform

DOI10.1090/memo/1158zbMath1380.28005arXiv1408.6979OpenAlexW2962899191MaRDI QIDQ5283811

Xavier Tolsa

Publication date: 25 July 2017

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.6979

zbMATH Keywords

Cauchy transformdensityrectifiabilitysquare function

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78)

Related Items (13)

Rectifiability of harmonic measure ⋮ Wasserstein distance and the rectifiability of doubling measures. I ⋮ Wasserstein distance and the rectifiability of doubling measures. II ⋮ A square function involving the center of mass and rectifiability ⋮ Characterization of \(n\)-rectifiability in terms of Jones' square function. II ⋮ Integral Menger curvature and rectifiability of $n$-dimensional Borel sets in Euclidean $N$-space ⋮ An \(\alpha\)-number characterization of \(L^p\) spaces on uniformly rectifiable sets ⋮ The Riesz transform and quantitative rectifiability for general Radon measures ⋮ Characterization of rectifiable measures in terms of 𝛼-numbers ⋮ Analytic capacity and projections ⋮ Geometric conditions for the \(L^2\)-boundedness of singular integral operators with odd kernels with respect to measures with polynomial growth in \(\mathbb{R}^d\) ⋮ Sufficient condition for rectifiability involving Wasserstein distance \(W_2\) ⋮ A family of singular integral operators which control the Cauchy transform

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