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

DOI10.1090/S0894-0347-02-00401-0zbMath1016.30020MaRDI QIDQ4780394

Joan Mateu, Joan Verdera, Xavier Tolsa

Publication date: 19 November 2002

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Cauchy integralCantor setanalytic capacity\(T(b)\)-theorempositive analytic capacity

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Capacity and harmonic measure in the complex plane (30C85)

Related Items (10)

Painlevé's problem and the semiadditivity of analytic capacity. ⋮ Quasiconformal maps, analytic capacity, and non linear potentials ⋮ The precise representative for the gradient of the Riesz potential of a finite measure ⋮ Calderón-Zygmund capacities and Wolff potentials on Cantor sets ⋮ Capacities associated with Calderón-Zygmund kernels ⋮ Cauchy transforms of self-similar measures: Starlikeness and univalence ⋮ Cauchy independent measures and almost-additivity of analytic capacity ⋮ Measures that define a compact Cauchy transform ⋮ Symmetry theorems and uniform rectifiability ⋮ The power law for the Buffon needle probability of the four-corner Cantor set

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