Quantitative Carleson's conjecture for Ahlfors regular domains

2025/05/15 by Emily Casey, Xavier Tolsa, Casey, Emily +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.10666

openalex publication_date 2025/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove a quantitative version of Carleson's ε² conjecture in higher dimension: we characterise those Ahlfors-David regular domains in ℝⁿ⁺¹ for which the Carleson's coefficients satisfy the so-called strong geometric lemma.

Citations

• The regularity problem for the Laplace equation in rough domains
• Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions

Related

• Quantitative control on the Carleson ε-function determines regularity
• Two quantitative versions of the Nonlinear Carleson Conjecture
• Carleson's ε² conjecture in higher dimensions
• Carleson Perturbations for the Regularity Problem
• A remark on Carleson measures of domains in ℂⁿ