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The Cauchy integral,
analytic capacity and subsets of quasicircles
Xiang Fang |
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Vol. 166 (1994), No. 2, 247–294
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Abstract |
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In this paper, we show that if K ⊂ ℂ is AD-regular and sufficiently flat, then K is a subset of a chord-arc curve if the Cauchy integral operator is bounded on L2(K). This result partially answers a question raised by G. David, P. Jones and S. Semmes. Also, we prove that if K is as above (locally) and has positive analytic capacity, then K must contain a subset of a rectifiable curve of positive length. Finally, we characterize subsets of some quasicircles in terms of a simple geometric condition invented by P. Jones. |
Mathematical Subject Classification 2000
Primary: 30E20
Secondary: 30C85
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Milestones
Received: 10 August 1992
Revised: 1 March 1993
Accepted: 16 March 1993
Published: 1 December 1994
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Authors |
| Xiang Fang | |
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