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


32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32T99 Pseudoconvex domains
Full Text: DOI EuDML


[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
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.