Arkiv för Matematik

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

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

Joan Verdera

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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.

Article information

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

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

Permanent link to this document
http://projecteuclid.org/euclid.afm/1485898673

Digital Object Identifier
doi:10.1007/BF02384497

Zentralblatt MATH identifier
1039.42011

Rights
2000 © Institut Mittag-Leffler

Citation

Verdera, Joan. On the T (1)-theorem for the Cauchy integral. Ark. Mat. 38 (2000), no. 1, 183--199. doi:10.1007/BF02384497. http://projecteuclid.org/euclid.afm/1485898673.


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