Abstract
The main goal of this paper is to present an alternative, real variable proof of theT(1)-theorem for the Cauchy integral. We then prove that the estimate from below of analytic capacity in terms of total Menger curvature is a direct consequence of theT(1)-theorem. An example shows that theL ∞-BMO estimate for the Cauchy integral does not follow fromL 2 boundedness when the underlying measure is not doubling.
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Verdera, J. On theT(1)-theorem for the Cauchy integral. Ark. Mat. 38, 183–199 (2000). https://doi.org/10.1007/BF02384497
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DOI: https://doi.org/10.1007/BF02384497