Solution of the ∂ ¯ -equation on non-smooth strictly q -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem

Gerd Schmalz

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)

  • Volume: 18, Issue: 1, page 67-82
  • ISSN: 0391-173X

How to cite

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Schmalz, Gerd. "Solution of the $\bar{\partial }$-equation on non-smooth strictly $q$-concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18.1 (1991): 67-82. <http://eudml.org/doc/84096>.

@article{Schmalz1991,
author = {Schmalz, Gerd},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {g-concavity; finiteness of cohomology group},
language = {eng},
number = {1},
pages = {67-82},
publisher = {Scuola normale superiore},
title = {Solution of the $\bar\{\partial \}$-equation on non-smooth strictly $q$-concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem},
url = {http://eudml.org/doc/84096},
volume = {18},
year = {1991},
}

TY - JOUR
AU - Schmalz, Gerd
TI - Solution of the $\bar{\partial }$-equation on non-smooth strictly $q$-concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1991
PB - Scuola normale superiore
VL - 18
IS - 1
SP - 67
EP - 82
LA - eng
KW - g-concavity; finiteness of cohomology group
UR - http://eudml.org/doc/84096
ER -

References

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  1. [1] A. Andreotti - H. Grauert, Théorèms de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France90 (1962), 193-259. Zbl0106.05501MR150342
  2. [2] A. Andreotti - E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math., 25, 1965. Zbl0138.06604MR175148
  3. [3] G.M. Henkin, H. Lewy's equation and analysis on pseudoconvex manifolds (Russian), I. Uspekhi Mat. Nauk32 (1977), no. 3, 57-118; II. Mat. Sb.82 (1977), 300-308. Zbl0382.35038MR454067
  4. [4] G.M. Henkin - J. Leiterer, Theory of Functions on Complex Manifolds, Math. Monograph.60, Akademie-VerlagBerlin1984. Zbl0726.32001MR795028
  5. [5] G.M. Henkin - J. Leiterer, The Andreotti-Grauert Theory by Integral Formulas, Progress in Mathematics74, Akademie-VerlagBerlin1988. Zbl0654.32002MR968893
  6. [6] I. Lieb, Beschränkte Lösungen der Cauchy-Riemannschen Differentialgleichungen auf q-konkaven Gebieten, Manuscripta Math.26 (1979), 387-409. Zbl0395.32010MR520109
  7. [7] Chr. Laurent-Thiébaut - J. Leiterer, The Andreotti-Vesentini separation theorem with Ck estimates and extension of CR-forms, Preprint P-Math-13/89 Karl-Weierstrass-Institut für Mathematik, Berlin1989. MR1207871
  8. [8] N Øvrelid, Pseudodifferential Operators and the ∂-equation, Springer Lecture Notes, 512 (1976), 185-192. Zbl0325.58016
  9. [9] J. Milnor, Lectures on the h-cobordism theorem, Princeton University Press, Princeton, New Jersey1965. Zbl0161.20302MR190942
  10. [10] G. Schmalz, Solution of the ∂-equation with uniform estimates on strictly q-convex domains with non-smooth boundary, Math. Z.202, 1989, 409-430. Zbl0662.32017

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