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

Mateu, Joan; Tolsa, Xavier; Verdera, Joan

doi:10.1090/S0894-0347-02-00401-0

The planar Cantor sets of zero analytic capacity and the local -Theorem

Authors: Joan Mateu, Xavier Tolsa and Joan Verdera
Journal: J. Amer. Math. Soc. 16 (2003), 19-28
MSC (2000): Primary 30C85; Secondary 42B20, 30E20
DOI: https://doi.org/10.1090/S0894-0347-02-00401-0
Published electronically: July 10, 2002
MathSciNet review: 1937197
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Abstract: In this paper we obtain rather precise estimates for the analytic capacity of a big class of planar Cantors sets. In fact, we show that analytic capacity and positive analytic capacity are comparable for these sets. The main tool for the proof is an appropriate version of the -Theorem.

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