Quantitative Carleson's conjecture for Ahlfors regular domains

Abstract

In this article, we prove a quantitative version of Carleson's ${\epsilon }^2$ 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.

30 pages, 3 figures. V2: typos and small errors corrected; minor adjustments in the proof Proposition 3.1. Accepted for publication in Analysis & PDE