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Journal d'Analyse Mathématique

, Volume 135, Issue 1, pp 185–202 | Cite as

On the analytic and Cauchy capacities

  • Malik Younsi
Article
  • 26 Downloads

Abstract

We give new sufficient conditions for a compact set E ⊆ C to satisfy γ(E) = γc(E), where γ is the analytic capacity and γc is the Cauchy capacity. As a consequence, we provide examples of compact plane sets such that the above equality holds but the Ahlfors function is not the Cauchy transform of any complex Borel measure supported on the set.

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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  1. 1.Department of MathematicsStony Brook UniversityStony BrookUSA

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