On theT(1)-theorem for the Cauchy integral

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.