Capacities associated with Calderón-Zygmund kernels

DOI10.1007/s11118-012-9301-1zbMath1271.42016arXiv1112.3849OpenAlexW1982858928MaRDI QIDQ1949222

Xavier Tolsa, Laura Prat, Joan Mateu, Vasilis Chousionis

Publication date: 6 May 2013

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3849

zbMATH Keywords

Calderón-Zygmund kernelAnalytic capacity

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Capacity and harmonic measure in the complex plane (30C85)

Related Items (4)

Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability ⋮ Symmetrization of a Cauchy-like kernel on curves ⋮ A family of singular integral operators which control the Cauchy transform ⋮ Singular integrals unsuitable for the curvature method whose \(L^2\)-boundedness still implies rectifiability

Cites Work

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• Calderón-Zygmund kernels and rectifiability in the plane
• Analytic capacity and differentiability properties of finely harmonic functions
• Removable sets of analytic functions satisfying a Lipschitz condition
• Unrectifiable 1-sets have vanishing analytic capacity
• The Riesz kernels do not give rise to higher dimensional analogues of the Menger-Melnikov curvature
• Menger curvature and rectifiability
• \(L^2\) boundedness of the Cauchy transform implies \(L^2\) boundedness of all Calderón-Zygmund operators associated to odd kernels
• Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
• Painlevé's problem and the semiadditivity of analytic capacity.
• On geometric properties of harmonic \(\text{Lip}_ 1\)-capacity
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Bilipschitz maps, analytic capacity, and the Cauchy integral
• Analytic capacity and measure
• Bounded analytic functions
• A nicely behaved singular integral on a purely unrectifiable set
• Capacities associated with scalar signed Riesz kernels, and analytic capacity
• Homogeneous Partial Derivatives of Radial Functions
• On the analytic capacity gamma_+
• The planar Cantor sets of zero analytic capacity and the local 𝑇(𝑏)-Theorem
• The semiadditivity of continuous analytic capacity and the inner boundary conjecture
• Analytic capacity: discrete approach and curvature of measure
• The analytic capacity of sets in problems of approximation theory

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