Hausdorff measure and capacity associated with Cauchy potentials

DOI10.1007/BF02312776zbMath0919.28004OpenAlexW2168336626MaRDI QIDQ1280617

K. Appert

Publication date: 15 August 1999

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02312776

zbMATH Keywords

Cantor setHausdorff measureanalytic capacityCauchy potentials

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Capacity and harmonic measure in the complex plane (30C85) Hausdorff and packing measures (28A78) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (2)

The planar Cantor sets of zero analytic capacity and the local 𝑇(𝑏)-Theorem ⋮ Large sets of zero analytic capacity

Cites Work

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• A real variable method for the Cauchy transform, and analytic capacity
• On the analytic capacity and curvature of some Cantor sets with non-\(\sigma\)-finite length
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Analytic capacity and measure
• A class of sets with positive length and zero analytic capacity
• Construction of H ¹ Functions concerning the Estimate of Analytic Capacity
• Cotlar's inequality without the doubling condition and existence of principal values for the Cauchy integral of measures

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