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Quantitative Carleson's conjecture for Ahlfors regular domains

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arxiv 2505.10666 v1 pith:C2DTM74D submitted 2025-05-15 math.CA math.AP

Emily Casey , Xavier Tolsa , Michele Villa This is my paper
classification math.CAmath.AP
keywords carlesonconjecturedomainsquantitativeregularahlforsahlfors-davidarticle
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abstract

In this article, we prove a quantitative version of Carleson's $\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the so-called strong geometric lemma.

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  1. Interactions between quantitative rectifiability, singular integrals, and boundary value problems for harmonic functions

    math.CA 2026-07 unverdicted novelty 1.0 of 10

    A field survey showing that quantitative rectifiability underpins results on Riesz transforms, removable sets, harmonic measure, and L^p boundary value problems for the Laplacian.

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