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

Joan Verdera Department of Mathematics, Universitat Autònoma de Barcelona

TBD mathscidoc:1701.332937

Arkiv for Matematik, 38, (1), 183-199, 1998.6
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$L$^{2}boundedness when the underlying measure is not doubling.
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  title={On the$T$(1)-theorem for the Cauchy integral},
  author={Joan Verdera},
  booktitle={Arkiv for Matematik},
Joan Verdera. On the$T$(1)-theorem for the Cauchy integral. 1998. Vol. 38. In Arkiv for Matematik. pp.183-199. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203558828683746.
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