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[B-F1] Bedford, E., Fornaess, J.E.: Biholomorphic maps of weakly pseudoconvex domains. Duke Math. J.45, 711–719 (1979)
[B-F2] Bedford, E., Fornaess, J.E.: A construction of peak functions on weakly pseudoconvex domains. Ann. Math.107, 555–568 (1978)
[Bi] Bishop, E.: A minimal boundary for function algebras. Pac. J. Math.9, 629–642 (1959)
[Ca] Catlin, D.: Estimates of invariant metrics on pseudoconvex domains of dimension two. Math. Z.200, 429–466 (1989)
[D-F1] Diederich, K., Fornaess, J.E.: Proper holomorphic maps onto pseudoconvex domains with real-analytic boundary. Ann. Math.110, 575–592 (1979)
[D-F2] Diederich, K., Fornaess, J.E.: Comparison of the Kobayashi and the Bergman metric. Math. Ann.254, 257–262 (1980)
[D-F-H] Diederich, K., Fornaess, J.E., Herbort, G.: Boundary Behavior of the Bergman Metric. Proc. Symp. Pure Math.41, 59–67 (1984)
[D-L] Diederich, K., Lieb, I.: Konvexität in der Komplexen Analysis. (DMV-Seminar, vol. 2) Basel Boston Stuttgart: Birkhäuser 1981
[F-S] Fornaess, J.E., Sibony, N.: Construction of p.s.h. functions on weakly pseudoconvex domains. Duke Math. J.58, 633–655 (1989)
[Gr] Graham, I.: Boundary Behavior of the Caratheodory and Kobayashi Metrics on Strongly Pseudoconvex Domains in ℂn With Smooth Boundary. Trans. Am. Math. Soc.207, 219–240 (1975)
[H] Henkin, G.: An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain. Dokl. Akad. Nauk SSSR210, 1026–1029 (1973); Soviet Math. Dokl.14, 858–862 (1973)
[Ha] Hahn, K. T.: Inequality Between the Bergman and the Caratheodory Differential Metric. Proc. Am. Math. Soc.68, 193–194 (1978)
[He1] Herbort, G.: Über das Randverhalten der Bergmanschen Kernfunktion und Metrik für eine spezielle Klasse schwach pseudokonvexer Gebiete des ℂn. Math. Z.184, 193–202 (1983)
[He2] Herbort, G.: The Growth of the Bergman Kernel on Pseudoconvex Domains of Homogeneous Finite Diagonal Type. (Preprint 1991)
[Hö] Hörmander, L.:L 2-estimates and existence theorems for the\(\bar \partial - operator\). Acta Math.113, 89–152 (1965)
[K-N] Kohn, J.J., Nirenberg, L.: A Pseudoconvex Domain not Admitting a Holomorphic Support Function. Math. Ann.201, 265–268 (1973)
[M1] McNeal, J.: Local Geometry of Decoupled Pseudoconvex Domains. In: Complex Analysis. Proc. of the Intern. Workshop, Wuppertal 1990. (Aspects Math.) Braunschweig Wiesbaden. Vieweg 1991
[M2] McNeal, J.: Lower Bounds on the Bergman Metric Near a Point of Finite Type. Ann. Math. (to appear)
[N-S-W] Nagel, A., Stein, E., Wainger, S.: Balls and metrics defined by vector fields I: Basic properties. Acta Math.155, 103–147 (1985)
[N] Noell, A.: Peak functions for pseudoconvex domains in ℂn. In: Proc. of the Special Year in Several Complex Variables at the Mittag-Leffler Institute. (Math. Notes, Princeton) (to appear)
[Ra1] Range, M.: Hölder estimates for\(\bar \partial u = f\) on weakly pseudoconvex domains. In: Proc. of Interntl. Conferences, Cortona, Italy, 1976-77, pp. 247–267. Pisa: Scuola Sup. Normale 1978
[Ra2] Range, M.: The Caratheodory metric and holomorphic maps on a class of weakly pseudoconvex domains. Pac. J. Math.78, 173–189 (1978)
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Herbort, G. Invariant metrics and peak functions on pseudoconvex domains of homogeneous finite diagonal type. Math Z 209, 223–243 (1992). https://doi.org/10.1007/BF02570831
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DOI: https://doi.org/10.1007/BF02570831