A result on extension of C.R. functions

Makhlouf Derridj; John Erik Fornaess

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 3, page 113-120
  • ISSN: 0373-0956

Abstract

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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 = λ f , ( 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 ) .

How to cite

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Derridj, Makhlouf, and Fornaess, John Erik. "A result on extension of C.R. functions." Annales de l'institut Fourier 33.3 (1983): 113-120. <http://eudml.org/doc/74592>.

@article{Derridj1983,
abstract = {Let $\Omega $ an open set in $\{\bf C\}^4$ 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)]) : $\bar\{\partial \}u=\lambda f$, ($f$ is a $(0,1)$ form, $\bar\{\partial \}$ closed in $U(z_0)$ in $U(z_0)$ with supp$(u)\subset \bar\{\Omega \}\cap U(z_0)$, then we deduce an extension result for $C.R.$ functions on $\partial \Omega \cap U(z_0)$, as holomorphic fonctions in $\Omega \cap V(z_0)$.},
author = {Derridj, Makhlouf, Fornaess, John Erik},
journal = {Annales de l'institut Fourier},
keywords = {extension of C. R. functions},
language = {eng},
number = {3},
pages = {113-120},
publisher = {Association des Annales de l'Institut Fourier},
title = {A result on extension of C.R. functions},
url = {http://eudml.org/doc/74592},
volume = {33},
year = {1983},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 3
SP - 113
EP - 120
AB - Let $\Omega $ an open set in ${\bf C}^4$ 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)]) : $\bar{\partial }u=\lambda f$, ($f$ is a $(0,1)$ form, $\bar{\partial }$ closed in $U(z_0)$ in $U(z_0)$ with supp$(u)\subset \bar{\Omega }\cap U(z_0)$, then we deduce an extension result for $C.R.$ functions on $\partial \Omega \cap U(z_0)$, as holomorphic fonctions in $\Omega \cap V(z_0)$.
LA - eng
KW - extension of C. R. functions
UR - http://eudml.org/doc/74592
ER -

References

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  8. [8] L. HÖRMANDER, Introduction to complex analysis in several variables, van Nostrand. Zbl0138.06203
  9. [9] L. HÖRMANDER, L²-estimates and existence theorems for the ∂-operator, Acta Math., 113 (1965). Zbl0158.11002MR31 #3691
  10. [10] J.J. KOHN and H. ROSSI, On the extension of holomorphic functions from the boundary of a complex manifold, Ann. Math., 81 (1965). Zbl0166.33802MR31 #1399
  11. [11] H. LEWY, On the local character... Ann. Math., 64 (1956). 
  12. [12] R. NIRENBERG, On the Lewy extension phenomenon, Trans. Amer. Math. Soc., 168 (1972). Zbl0241.32006MR46 #392
  13. [13] R.O. WELLS, On the local holomorphic hull... Comm. P.A.M., vol. XIX (1966). Zbl0142.33901

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