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Analyse non linéaire de l’opérateur défini par l’intégrale de Cauchy. (Nonlinear analysis of the operator defined by the Cauchy integral). (French) Zbl 0705.42011
The author considers a version C(a) of the Cauchy integral along the graph \(\Gamma_ a\) of a real-valued function A on \({\mathbb{R}}\) where \(A'=a\) and studies the analyticity of C(a) viewed as an operator valued functional in a. Necessary and sufficient conditions of boundedness in \(L^ 2({\mathbb{R}})\) of the multilinear operators of the Taylor expansion are also proved.
Reviewer: L.Goras

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
30F20 Classification theory of Riemann surfaces
Full Text: DOI Numdam EuDML
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