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Transactions of the American Mathematical Society

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Une minoration de la norme de l'opérateur de Cauchy sur les graphes lipschitziens

Author: Guy David
Journal: Trans. Amer. Math. Soc. 302 (1987), 741-750
MSC: Primary 42B20; Secondary 30C85
MathSciNet review: 891644
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Abstract: It was shown by T. Murai that the norm of the operator defined by the Cauchy kernel on the graph of a Lipschitz function $ A$ is less than $ C{(1 + {\left\Vert {A'} \right\Vert _\infty })^{1/2}}$. We use Garnett's example to show that this estimate is optimal.

References [Enhancements On Off] (What's this?)

  • [CMM] R. R. Coifman, A. McIntosh et Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur $ {L^2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), 361-387. MR 672839 (84m:42027)
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  • [M] T. Murai, Boundedness of singular integral operators of Calderon type VI, preprint series, College of General Education, Nagoya, no. 12, 1984. MR 846134 (88h:42019)
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Keywords: Lipschitz graph, Cauchy integral, Calderón-Zygmund operators
Article copyright: © Copyright 1987 American Mathematical Society

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