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

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- by Joan Mateu, Xavier Tolsa and Joan Verdera;
- J. Amer. Math. Soc.
**16**(2003), 19-28 - DOI: https://doi.org/10.1090/S0894-0347-02-00401-0
- Published electronically: July 10, 2002
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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 $T(b)$-Theorem.## References

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## Bibliographic Information

**Joan Mateu**- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, (Barcelona), Spain
**Xavier Tolsa**- Affiliation: Département de Mathématiques, Université de Paris Sud 91405 Orsay, cedex, France
- MR Author ID: 639506
- ORCID: 0000-0001-7976-5433
**Joan Verdera**- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, (Barcelona), Spain
- Received by editor(s): August 7, 2001
- Published electronically: July 10, 2002
- Additional Notes: The authors were partially supported by the grants BFM 2000-0361, HPRN-2000-0116 and 2001- SGR-00431. The second author was supported by a Marie Curie Fellowship of the European Union under contract HPMFCT-2000-00519.
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1937197