Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chin-Huei Chang; Hsuan-Pei Lee

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 1, page 21-37
  • ISSN: 0391-173X

Abstract

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The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for C k ∂ ¯ -closed forms at the critical degree, 0 ≤ k ≤ ∞ (Theorem 1.1). Part of Frenkel’s lemma in C k category is also proved.

How to cite

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Chang, Chin-Huei, and Lee, Hsuan-Pei. "Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.1 (2006): 21-37. <http://eudml.org/doc/241973>.

@article{Chang2006,
abstract = {The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for $C^k$$\{\bar\{\partial \}\}$-closed forms at the critical degree, $0\le k\le \infty $ (Theorem 1.1). Part of Frenkel’s lemma in $C^k$ category is also proved.},
author = {Chang, Chin-Huei, Lee, Hsuan-Pei},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {21-37},
publisher = {Scuola Normale Superiore, Pisa},
title = {Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree},
url = {http://eudml.org/doc/241973},
volume = {5},
year = {2006},
}

TY - JOUR
AU - Chang, Chin-Huei
AU - Lee, Hsuan-Pei
TI - Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2006
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 1
SP - 21
EP - 37
AB - The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for $C^k$${\bar{\partial }}$-closed forms at the critical degree, $0\le k\le \infty $ (Theorem 1.1). Part of Frenkel’s lemma in $C^k$ category is also proved.
LA - eng
UR - http://eudml.org/doc/241973
ER -

References

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  1. [1] C. H. Chang and H. P. Lee, Semi-global solution of ∂ ¯ b with L p ( 1 ≤ p ≤ ∞ ) bounds on strongly pseudoconvex real hypersurfaces in ℂ n ( n ≥ 3 ) , Publ. Mat. 43 (1999), 535–570. Zbl0954.32027MR1744621
  2. [2] C. H. Chang and H. P. Lee, Hartogs theorem for CR functions, Bull. Inst. Math. Acad. Sinica 32 (2004), 221–227. Zbl1072.32025MR2103960
  3. [3] J. E. Fornæss, Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math. 98 (1976), 529–569. Zbl0334.32020MR422683
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  9. [9] R. Narasimhan, “Several Complex Variables”, Chicago Lecture Notes in Math., The University of Chicago Press, 1971. Zbl0223.32001MR342725
  10. [10] M. R. Range, “Holomorphic Functions and Integral Representations in Several Complex Variables”, Springer-Verlag, New York, 1986. Zbl0591.32002MR847923
  11. [11] J. P. Rosay, Some application of Cauchy-Fantappié forms to (local) problems in ∂ ¯ b , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13 (1986), 225–243. Zbl0633.32007MR876123
  12. [12] Y. T. Siu, “Techniques of Extension of Analytic Objects”, Lecture Notes in Pure and Applied Math., Vol. 8, Marcel Dekker, 1974. Zbl0294.32007MR361154
  13. [13] Y. T. Siu and G. Trautmann, “Gap-sheaves and Extension of Coherent Analytic Subsheaves”, Lecture Notes in Mathematics, Vol. 172, Springer-Verlag, 1971. Zbl0208.10403MR287033
  14. [14] S. M. Webster, On the local solution of the tangential Cauchy-Riemann equations, Nonlinear Anal. 6 (1989), 167–182. Zbl0679.32019MR995503

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