Arkiv för Matematik

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  • Volume 38, Number 1 (2000), 183-199.

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

Joan Verdera

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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.

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Ark. Mat. Volume 38, Number 1 (2000), 183-199.

Received: 30 June 1998
First available in Project Euclid: 31 January 2017

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2000 © Institut Mittag-Leffler


Verdera, Joan. On the T (1)-theorem for the Cauchy integral. Ark. Mat. 38 (2000), no. 1, 183--199. doi:10.1007/BF02384497.

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