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

Soit Ω un ouvert de C n , de classe C 4 près de z 0 ∈∂Ω, λ 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 : ∂ ¯u=λf(f(0,1) forme donnée dans U(z 0 ), ∂ ¯ fermée) dans U(z 0 ) avec supp(u)⊂Ω ¯∩U(z 0 ), on déduit un résultat d’extension de fonctions C.R. sur ∂Ω∩U(z 0 ), en fonctions holomorphes dans Ω∩V(z 0 ).

Let Ω an open set in C 4 near z 0 ∈∂Ω, λ 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)]) : ∂ ¯u=λf, (f is a (0,1) form, ∂ ¯ closed in U(z 0 ) in U(z 0 ) with supp(u)⊂Ω ¯∩U(z 0 ), then we deduce an extension result for C.R. functions on ∂Ω∩U(z 0 ), as holomorphic fonctions in Ω∩V(z 0 ).

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     author = {Derridj, Makhlouf and Fornaess, John Erik},
     title = {A result on extension of {C.R.} functions},
     journal = {Annales de l'Institut Fourier},
     pages = {113--120},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {3},
     year = {1983},
     doi = {10.5802/aif.933},
     zbl = {0518.32010},
     mrnumber = {85f:32031},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.933/}
}
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Derridj, Makhlouf; Fornaess, John Erik. A result on extension of C.R. functions. Annales de l'Institut Fourier, Tome 33 (1983) no. 3, pp. 113-120. doi : 10.5802/aif.933. https://aif.centre-mersenne.org/articles/10.5802/aif.933/

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