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Sur le noyau de Bergman des domaines de Reinhardt. (French) Zbl 0489.32017


MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32T99 Pseudoconvex domains
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References:

[1] D’Angelo, J.: A note on the Bergman Kernel. Duke Math. Journal45, (no 2) 259-265 (1978) · Zbl 0384.32006
[2] Bell, S.: Biholomorphic mapping and the \(\bar \partial \) . Annals of Math.114, 103-113 (1981) · Zbl 0423.32009
[3] Bell, S., Boas, H.: Regularity of the Bergman projection in weakly pseudoconvex domains. Math. Ann.257, 23-30 (1981) · Zbl 0461.32007
[4] Bell, S., Ligocka, E.: A simplification and extension of Fefferman’s theorem on biholomorphic mappings. Invent. Math.57, 283-289 (1980) · Zbl 0421.32015
[5] Boichu, D.: Conjecture de Ramadanov sur le noyau de Bergman Thèse de 3ème cycle, Université de Lille I, juin 1982
[6] Bonami, A., Lohoue, N.: Projecteurs de Bergman et Szegö pour une classe de domaines faiblement pseudo-convexes et estimationsL p . Prépublications, Université de Paris-Sud
[7] Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. S.M.F. Astérisque34-35, 123-164 (1976) · Zbl 0344.32010
[8] Coeuré, G.: Sur le noyau de Bergman des domaines de Reinhart. Publication IRMA-Lille-Vol.3, (fasc. 5, II) 1-16 (1981)
[9] Diederich, K.: Some recent developments in the theory of the Bergman kernel function: a survey. Proceedings of Symposia in Pure Mathematics, Vol. 30 (1977) · Zbl 0352.32008
[10] Diederich, K., Fornaess, J.: Pseudo-convex domains with real-analytic boundary. Ann. of Math.107, 371-384 (1978) · Zbl 0378.32014
[11] Fefferman, C.: The Bergman Kernel and biholomorphic mapping of pseudoconvex domains. Invent. Math.26, 1-65 (1974) · Zbl 0289.32012
[12] Hörmander, L.: Introduction to complex analysis in several variables. North Holland, Amsterdam (1973) · Zbl 0271.32001
[13] Hörmander, L.:L 2-Estimates and existence theorems for the \(\bar \partial \) -operator. Acta Math.113, 89-152 (1965) · Zbl 0158.11002
[14] Kerzman, N.: The Bergman kernel function. Differentiability at the boundary. Math. Ann.195, 149-158 (1972)
[15] Kohn, J.J.: Harmonic integrals on strongly pseudo-convex manifolds I and II. Ann. Math.78, 112-148 (1963);79, 450-472 (1964) · Zbl 0161.09302
[16] Kohn, J.J.: Boundary behavior of \(\bar \partial \) on weakly pseudo-convex manifolds of dimension two. J. Differential Geometry6, 523-542 (1972) · Zbl 0256.35060
[17] Kohn, J.J.: Subellipticité of the \(\bar \partial \) Neumann problem on pseudo-convex domains sufficient conditions. Acta Math.142, 79-122 (1979) · Zbl 0395.35069
[18] Ramadanov, I.P.: A characterisation of the balls inC n by means of the Bergman kernel. Compte rendu de l’Académie bulgare des Sciences, Tome 34, (no 7) (1981)
[19] Skwarczynski, M.: Biholomorphic invariants related to the Bergman functions Wroclawska Drukarnia Naukowa, 1980 · Zbl 0443.32014
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