×

Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions. (English) Zbl 0353.32025


MSC:

32T99 Pseudoconvex domains
32L05 Holomorphic bundles and generalizations
32E10 Stein spaces
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Diederich, K., Fornæss, J.E.: Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains. Proc. Nat. Acad. Sci. USA72, 3279-3280 (1975) · Zbl 0309.32012
[2] Diederich, K., Fornæss, J.E.: A strange bounded smooth domain of holomorphy. Bull. Amer. Math. Soc.82, 75-76 (1976) · Zbl 0317.32020
[3] Diederich, K., Fornæss, J.E.: Pseudoconvex domains: An example with nontrivial nebenhuelle. Math. Ann.225, 275-292 (1977) · Zbl 0333.32018
[4] Diederich, K., Fornæss, J.E.: Pseudoconvex domains: Existence of Stein neighborhoods. To appear · Zbl 0661.32025
[5] Fischer, G.: Holomorph-vollständige Faserbündel. Math. Ann.180, 341-348 (1969) · Zbl 0167.36801
[6] Fischer, G.: Hilbert spaces of holomorphic functions on bounded domains. Manuscripta math.3, 305-314 (1970) · Zbl 0202.36601
[7] Fischer, G.: Fibrés holomorphes au-dessus d’un espace de Stein. Espaces analytiques, pp. 57-69, Bukarest 1971
[8] Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy Riemann complex. Ann. Math. Studies75, Princeton 1972 · Zbl 0247.35093
[9] Helms, L.L.: Introduction to potential theory. New York: Wiley 1969 · Zbl 0188.17203
[10] Hirschowitz, A.: Sur certains fibrés holomorphes à base et fibre de Stein (corrections). C.R. Hebd. Acad. Sci., série A-B278, 89-91 (1974) · Zbl 0291.32022
[11] Hirschowitz, A.: Domaines de Stein et fonctions holomorphes bornées. Math. Ann.213, 185-193 (1975) · Zbl 0289.32004
[12] Hörmander, L.: An Introduction to complex analysis in several variables. Amsterdam: Elsevier 1973 · Zbl 0271.32001
[13] Kohn, J.J., Nirenberg, L.: A pseudoconvex domain not admitting a holomorphic support function. Math. Ann.201, 265-268 (1973) · Zbl 0248.32013
[14] Königsberger, K.: Über die Holomorphie-Vollständigkeit lokaltrivialer Faserräume. Math. Ann.189, 178-184 (1970) · Zbl 0203.39001
[15] Krantz, St. G.: Optimal Lipschitz andL p-regularity for the equation \(\bar \partial u = f\) on strongly pseudoconvex domains. Math. Ann.219, 233-260 (1976) · Zbl 0311.35074
[16] Matsushima, Y., Morimoto, A.: Sur certains espaces fibrés sur une variété de Stein. Bull. Soc. Math. de France88, 137-155 (1960) · Zbl 0094.28104
[17] Pflug, P.: Glatte Holomorphiegebiete mit plurisubharmonischer innerer Randfunktion sind Banach-Stein. Ark. Math.14, 55-58 (1976) · Zbl 0319.32028
[18] Rossi, H.: A Docquier-Grauert lemma for strongly pseudoconvex domains in complex manifolds. Rocky Mount. J. Math. (1975)
[19] Serre, J-P.: Quelques problèmes globaux relatifs aux variétés de Stein. Colloque sur les fonctions de plusieurs variables, p. 57-68, Bruxelles 1958
[20] Siu, Y.-T.: All plane domains are Banach-Stein. Manuscripta math.14, 101-105 (1974) · Zbl 0294.32010
[21] Siu, Y.-T.: Holomorphic fiber bundles whose fibers are bounded Stein domains with zero first Betti number. Math. Ann.219, 171-192 (1976) · Zbl 0318.32010
[22] Stehlé, J.-L.: Fonctions plurisousharmoniques et convexité holomorphe de certains fibrés analytiques. C.R. Hebd. Acad. Sci. Sér. A-B279, 235-238 (1974)
[23] Stein, E.M.: Singular integrals and estimates for the Cauchy Riemann equations. Bull. Amer. Math. Soc.79, 440-445 (1973) · Zbl 0257.35040
[24] Stein, K.: Überlagerungen holomorph-vollständiger komplexer Räume. Arch. Math.1, 354-361 (1956) · Zbl 0072.08002
[25] Wells, R. O.: Function theory on differentiable submanifolds. In: Contrib. to Analysis, L. Bers, ed., Ahlfors. London-New York: Academic Press 1974 · Zbl 0293.32001
[26] Wu, H.: Normal families of holomorphic mappings. Acta Math.119, 193-233 (1967) · Zbl 0158.33301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.