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The Bergman kernel and biholomorphic mappings of pseudoconvex domains. (English) Zbl 0289.32012


MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32T99 Pseudoconvex domains
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References:

[1] Diederich, K.: Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten. Math. Ann.187, 9-36 (1970) · doi:10.1007/BF01368157
[2] Diederich, K.: Über die 1. und 2. Ableitungen der Bergmanschen Kernfunktion und ihr Randverhalten. Math. Ann.203, 129-170 (1973) · Zbl 0253.32011 · doi:10.1007/BF01431441
[3] Folland, G. B., Kohn, J. J.: The Neumann Problem for the Cauchy-Riemann Complex. Princeton University Press 1972 · Zbl 0247.35093
[4] Folland, G. B., Stein, E. M.: Parametrices and estimates for the \(\bar \partial \) b-complex on strongly pseudoconvex boundaries. Bulletin A.M.S. (to appear) · Zbl 0294.35059
[5] Graham, I.: Boundary behavior of the Carathéodory, Kobayashi, and Bergman metrics on strongly pseudoconvex domains inC n with smooth boundaries. Bulletin A.M.S.79, 749-751 (1973) · Zbl 0267.32011 · doi:10.1090/S0002-9904-1973-13297-5
[6] Grauert, H.: Lecture given at a conference on several complex variables. Paris 1972
[7] Hörmander, L.:L 2 estimates and existence theorems for the \(\bar \partial \) -operator. Acta Math.113, 89-152 (1965) · Zbl 0158.11002 · doi:10.1007/BF02391775
[8] Hörmander, L.: The boundary behavior of the Bergman kernel (preprint)
[9] Kerzman, N.: The Bergman kernel function: differentiability at the boundary. Math. Ann.195, 149-158 (1972) · doi:10.1007/BF01419622
[10] Siegel, C.L., Moser, J.: Celestial Mechanics. Springer 1972
[11] Stein, E. M.: Boundary Behavior of Holomorphic Functions of Several Complex Variables Princeton University Press 1972 · Zbl 0242.32005
[12] Vormoor, N.: Topologische Fortsetzung biholomorpher Funktionen auf dem Rande bei beschränkten streng-pseudokonvexen Gebieten im ?m mitC ?-Rand. Math. Ann.204, 239-269 (1973) · Zbl 0259.32006 · doi:10.1007/BF01351592
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