A result on extension of C.R. functions
Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 113-120.

Let $\Omega$ an open set in ${\mathbf{C}}^{4}$ near ${z}_{0}\in \partial \Omega$, $\lambda$ a suitable holomorphic function near ${z}_{0}$. If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : $\overline{\partial }u=\lambda f$, ($f$ is a $\left(0,1\right)$ form, $\overline{\partial }$ closed in $U\left({z}_{0}\right)$ in $U\left({z}_{0}\right)$ with supp$\left(u\right)\subset \overline{\Omega }\cap U\left({z}_{0}\right)$, then we deduce an extension result for $C.R.$ functions on $\partial \Omega \cap U\left({z}_{0}\right)$, as holomorphic fonctions in $\Omega \cap V\left({z}_{0}\right)$.

Soit $\Omega$ un ouvert de ${\mathbf{C}}^{n}$, de classe ${C}^{4}$ près de ${z}_{0}\in \partial \Omega$, $\lambda$ une fonction holomorphe convenable près de ${z}_{0}$. Sachant que l’on sait résoudre (voir [M. Derridj, Annali.Sci. Norm. Pisa, Série IV, vol. IX (1981)]) le problème : $\overline{\partial }u=\lambda f\left(f\left(0,1\right)$ forme donnée dans $U\left({z}_{0}\right)$, $\overline{\partial }$ fermée) dans $U\left({z}_{0}\right)$ avec supp$\left(u\right)\subset \overline{\Omega }\cap U\left({z}_{0}\right)$, on déduit un résultat d’extension de fonctions $C.R.$ sur $\partial \Omega \cap U\left({z}_{0}\right)$, en fonctions holomorphes dans $\Omega \cap V\left({z}_{0}\right)$.

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title = {A result on extension of {C.R.} functions},
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Derridj, Makhlouf; Fornaess, John Erik. A result on extension of C.R. functions. Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 113-120. doi : 10.5802/aif.933. http://archive.numdam.org/articles/10.5802/aif.933/

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