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

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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.
Original languageEnglish
Pages (from-to)183-199
JournalArkiv for Matematik
Volume38
Issue number1
DOIs
Publication statusPublished - 1 Jan 2000

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