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Non-vanishing of the Bergman kernel function at boundary points of certain domains in \(\mathbb{C}^n\). (English) Zbl 0398.32014


MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32T99 Pseudoconvex domains
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:

[1] Bergman, S.: The kernel function and conformal mapping. A.M.S. Survey V, 2. ed. Providence 1970 · Zbl 0208.34302
[2] Diederich, K., Fornaess, J.: Pseudoconvex domains with realanalytic boundary. Ann. of Math.107, 371-384 (1978) · Zbl 0378.32014 · doi:10.2307/1971120
[3] Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26, 1-65 (1974) · Zbl 0289.32012 · doi:10.1007/BF01406845
[4] Folland, G., Kohn, J.: The Neumann problem for the Cauchy-Riemann complex. Ann. of Math. Studies, No. 75. Princeton: University Press 1972 · Zbl 0247.35093
[5] Hörmander, L.: The boundary behavior of the Bergman kernel. (unpublished manuscript)
[6] Kerzman, N.: The Bergman kernel function. Differentiability at the boundary. Math. Ann.195, 149-158 (1972) · doi:10.1007/BF01419622
[7] Kohn, J.: Sufficient conditions for subellipticity on weakly pseudoconvex domains. Proc. Nat. Acad. Sci. USA74, 2214-2216 (1977) · Zbl 0349.35011 · doi:10.1073/pnas.74.6.2214
[8] Webster, S.: Biholomorphic mappings and the Bergman kernel off the diagonal. Preprint · Zbl 0385.32019
[9] Ligocka, E.: Some remarks on extension of biholomorphic mappings. (to appear) · Zbl 0458.32008
[10] Ligocka, E.: How to prove Fefferman’s theorem without use of differential geometry. Ann. Polish Math. (to appear) · Zbl 0489.32016
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