Harmonic measure and Riesz transform in uniform and general domains

DOI10.1515/crelle-2017-0037zbMath1436.31019arXiv1509.08386OpenAlexW2964105710MaRDI QIDQ2282295

Mihalis Mourgoglou, Xavier Tolsa

Publication date: 7 January 2020

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.08386

zbMATH Keywords

harmonic measureRiesz transformuniform domain

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Harmonic analysis and PDEs (42B37)

Related Items (12)

BMO solvability and absolute continuity of caloric measure ⋮ \(A_\infty\) implies NTA for a class of variable coefficient elliptic operators ⋮ On harmonic measure and rectifiability in uniform domains ⋮ The two-phase problem for harmonic measure in VMO ⋮ Corona decompositions for parabolic uniformly rectifiable sets ⋮ A two-phase free boundary problem for harmonic measure and uniform rectifiability ⋮ \(L^2\)-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type ⋮ Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem ⋮ BMO solvability and absolute continuity of harmonic measure ⋮ Tangent measures of elliptic measure and applications ⋮ Quantitative absolute continuity of harmonic measure and the Dirichlet problem: a survey of recent progress ⋮ Square function estimates, the BMO Dirichlet problem, and absolute continuity of harmonic measure on lower-dimensional sets

Cites Work

• Unnamed Item
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• Rectifiability of harmonic measure
• Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory
• The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions
• On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
• Harmonic measure and approximation of uniformly rectifiable sets
• A new characterization of chord-arc domains
• Characterization of \(n\)-rectifiability in terms of Jones' square function. II
• Doubling conditions for harmonic measure in John domains
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Removable sets for Lipschitz harmonic functions in the plane
• On the Hausdorff dimension of harmonic measure in higher dimension
• The \(Tb\)-theorem on non-homogeneous spaces.
• Uniform rectifiability and harmonic measure. II: Poisson kernels in \(L^p\) imply uniform rectifiability
• Bilipschitz maps, analytic capacity, and the Cauchy integral
• Uniform Rectifiability and Harmonic Measure III: Riesz Transform Bounds Imply Uniform Rectifiability of Boundaries of 1-sided NTA Domains
• Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$
• Equivalence between the boundary Harnack principle and the Carleson estimate
• Potential theory
• Boundary Harnack principle and Martin boundary for a uniform domain

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