Trace de Cauchy pour certaines fonctions localement intégrables sur ouvert borné de C

• Autores: Iban Harloluchet
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 48, Nº 1, 2004, págs. 69-102
• Idioma: inglés
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• Resumen

  • Let Ω be a bounded open subset of C, and let f be a distribution on Ω such that ∂f is a Radon measure of finite total mass. By means of the Cauchy transform, we introduce the “Cauchy trace” of f, which takes values in the set of analytic functionals on the boundary ∂Ω of Ω. The properties of this application are studied in detail. For instance, the characterization of its kernel is discussed according to the properties of the boundary ∂Ω. Roughly speaking, the Cauchy trace allows us to interpret the Cauchy-Pompeiu formula in the same way as the Sobolev trace allows tointerpret the Stokes formula.