On the T(1)-theorem for the Cauchy integral

Abstract

The main goal of this paper is to present an alternative, real variable proof of the T(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 the T(1)-theorem. An example shows that the L^∞-BMO estimate for the Cauchy integral does not follow from L² boundedness when the underlying measure is not doubling.