References
Diederich, K., Fornæss, J.E.: Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains. Proc. Nat. Acad. Sci. USA72, 3279–3280 (1975)
Diederich, K., Fornæss, J.E.: A strange bounded smooth domain of holomorphy. Bull. Amer. Math. Soc.82, 75–76 (1976)
Diederich, K., Fornæss, J.E.: Pseudoconvex domains: An example with nontrivial nebenhuelle. Math. Ann.225, 275–292 (1977)
Diederich, K., Fornæss, J.E.: Pseudoconvex domains: Existence of Stein neighborhoods. To appear
Fischer, G.: Holomorph-vollständige Faserbündel. Math. Ann.180, 341–348 (1969)
Fischer, G.: Hilbert spaces of holomorphic functions on bounded domains. Manuscripta math.3, 305–314 (1970)
Fischer, G.: Fibrés holomorphes au-dessus d'un espace de Stein. Espaces analytiques, pp. 57–69, Bukarest 1971
Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy Riemann complex. Ann. Math. Studies75, Princeton 1972
Helms, L.L.: Introduction to potential theory. New York: Wiley 1969
Hirschowitz, A.: Sur certains fibrés holomorphes à base et fibre de Stein (corrections). C.R. Hebd. Acad. Sci., série A-B278, 89–91 (1974)
Hirschowitz, A.: Domaines de Stein et fonctions holomorphes bornées. Math. Ann.213, 185–193 (1975)
Hörmander, L.: An Introduction to complex analysis in several variables. Amsterdam: Elsevier 1973
Kohn, J.J., Nirenberg, L.: A pseudoconvex domain not admitting a holomorphic support function. Math. Ann.201, 265–268 (1973)
Königsberger, K.: Über die Holomorphie-Vollständigkeit lokaltrivialer Faserräume. Math. Ann.189, 178–184 (1970)
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)
Matsushima, Y., Morimoto, A.: Sur certains espaces fibrés sur une variété de Stein. Bull. Soc. Math. de France88, 137–155 (1960)
Pflug, P.: Glatte Holomorphiegebiete mit plurisubharmonischer innerer Randfunktion sind Banach-Stein. Ark. Math.14, 55–58 (1976)
Rossi, H.: A Docquier-Grauert lemma for strongly pseudoconvex domains in complex manifolds. Rocky Mount. J. Math. (1975)
Serre, J-P.: Quelques problèmes globaux relatifs aux variétés de Stein. Colloque sur les fonctions de plusieurs variables, p. 57–68, Bruxelles 1958
Siu, Y.-T.: All plane domains are Banach-Stein. Manuscripta math.14, 101–105 (1974)
Siu, Y.-T.: Holomorphic fiber bundles whose fibers are bounded Stein domains with zero first Betti number. Math. Ann.219, 171–192 (1976)
Stehlé, J.-L.: Fonctions plurisousharmoniques et convexité holomorphe de certains fibrés analytiques. C.R. Hebd. Acad. Sci. Sér. A-B279, 235–238 (1974)
Stein, E.M.: Singular integrals and estimates for the Cauchy Riemann equations. Bull. Amer. Math. Soc.79, 440–445 (1973)
Stein, K.: Überlagerungen holomorph-vollständiger komplexer Räume. Arch. Math.1, 354–361 (1956)
Wells, R. O.: Function theory on differentiable submanifolds. In: Contrib. to Analysis, L. Bers, ed., Ahlfors. London-New York: Academic Press 1974
Wu, H.: Normal families of holomorphic mappings. Acta Math.119, 193–233 (1967)
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During the preparation of this paper the second author has been partially supported by an NSF grant and by an NAVF grant from Norway
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Diederich, K., Fornæss, J.E. Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions. Invent Math 39, 129–141 (1977). https://doi.org/10.1007/BF01390105
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DOI: https://doi.org/10.1007/BF01390105