, Volume 38, Issue 1, pp 183-199

On theT (1)-theorem for the Cauchy integral

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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.