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 ΩU(z 0 ), en fonctions holomorphes dans ΩV(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 ΩU(z 0 ), as holomorphic fonctions in ΩV(z 0 ).

@article{AIF_1983__33_3_113_0,
     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},
     mrnumber = {85f:32031},
     zbl = {0518.32010},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.933/}
}
TY  - JOUR
AU  - Derridj, Makhlouf
AU  - Fornaess, John Erik
TI  - A result on extension of C.R. functions
JO  - Annales de l'Institut Fourier
PY  - 1983
SP  - 113
EP  - 120
VL  - 33
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.933/
DO  - 10.5802/aif.933
LA  - en
ID  - AIF_1983__33_3_113_0
ER  - 
%0 Journal Article
%A Derridj, Makhlouf
%A Fornaess, John Erik
%T A result on extension of C.R. functions
%J Annales de l'Institut Fourier
%D 1983
%P 113-120
%V 33
%N 3
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.933/
%R 10.5802/aif.933
%G en
%F AIF_1983__33_3_113_0
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. http://www.numdam.org/articles/10.5802/aif.933/

[1] A. Andreotti and C.D. Hill, E.E. convexity and the H. Lewy problem. Part I : Reduction to vanishing theorems, Ann. Scuola Normale Sup. di Pisa, 26 (1972). | Numdam | Zbl

[2] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. IHES, vol. 24-25. | Numdam | MR | Zbl

[3] M.S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. Math., 113 (1981). | MR | Zbl

[4] E. Bedford and J.E. Fornaess, Local extension of C.R. function from weakly pseudoconvex boundaries, Michigan Math. J., 25. | MR | Zbl

[5] A. Bogges, C.R. extendability near a point where the first leviform vanishes, Duke Math. J., 43 (3). | Zbl

[6] M. Derridj, Inégalités de Carleman et extension locale des fonctions holomorphes, Annali. Sci. Norm. Pisa, Serie IV vol. IX (1981). | Numdam | Zbl

[7] C.D. Hill and Taïani, Families of analytic discs in Cn with boundaries on a prescribed C.R. submanifold, Ann. Scuola Norm. Pisa, 4-5 (1978). | Numdam | Zbl

[8] L. Hörmander, Introduction to complex analysis in several variables, van Nostrand. | Zbl

[9] L. Hörmander, L²-estimates and existence theorems for the ∂-operator, Acta Math., 113 (1965). | MR | Zbl

[10] J.J. Kohn and H. Rossi, On the extension of holomorphic functions from the boundary of a complex manifold, Ann. Math., 81 (1965). | MR | Zbl

[11] H. Lewy, On the local character... Ann. Math., 64 (1956).

[12] R. Nirenberg, On the Lewy extension phenomenon, Trans. Amer. Math. Soc., 168 (1972). | MR | Zbl

[13] R.O. Wells, On the local holomorphic hull... Comm. P.A.M., vol. XIX (1966). | Zbl

Cité par Sources :