Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in 𝐂 2
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 7 (1998) no. 1, pp. 51-85.
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     author = {Kamimoto, Joe},
     title = {Asymptotic expansion of the {Bergman} kernel for weakly pseudoconvex tube domains in ${\bf C}^2$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {51--85},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
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     volume = {Ser. 6, 7},
     number = {1},
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     mrnumber = {1658444},
     zbl = {0917.32018},
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     url = {http://archive.numdam.org/item/AFST_1998_6_7_1_51_0/}
}
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Kamimoto, Joe. Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in ${\bf C}^2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 7 (1998) no. 1, pp. 51-85. http://archive.numdam.org/item/AFST_1998_6_7_1_51_0/

[1] Aladro (G.) .- The compatibly of the Kobayashi approach region and the admissible approach region, Illinois J. Math. 33 (1989), pp. 27-41 . | MR | Zbl

[2] Bergman (S.) .- Zur Theorie von pseudokonformen Abbildungen, Math. Sbornik. Akad. Nauk SSSR (1936), pp. 79-96. | JFM | Zbl

[3] Boas (H.P.), Fu (S.) and Straube (E.J.) .- The Bergman kernel function: Explicit formulas and zeros, prepint.

[4] Boas (H.P.), Straube (E.J.) and Yu (J.) .- Boundary limits of the Bergman kernel and metric, Michigan Math. J. 42 (1995), pp. 449-461. | MR | Zbl

[5] Boichu (D.) and Cœuré (G.) .- Sur le noyau de Bergman des domaines de Reinhardt, Invent. Math. 72 (1983), pp. 131-152. | MR | Zbl

[6] Bonami (A.) and Lohoué (N.) .- Projecteurs de Bergman et Szegö pour une classe de domaines faiblement pseudo-convexes et estimation Lp, Compositio Math. 46, n° 2 (1982), pp. 159-226. | Numdam | MR | Zbl

[7] Boutet De Monvel (L.) and Sjöstrand (J.) .- Sur la singularité des noyaux de Bergman et de Szegö, Soc. Math. de France Astérique 34-35 (1976), pp. 123-164. | Numdam | MR | Zbl

[8] Catlin (D.) .- Estimates of invariant metric on pseudoconvex domains of dimension two, Math. Z. 200 (1989), pp. 429-266. | MR | Zbl

[9] Chalmers (B.L.) . - On boundary behavior of the Bergman kernel function and related domain functionals, Pacific J. Math. 29 (1969), pp. 243-250. | MR | Zbl

[10] Cho (S.) . - Boundary behavior of the Bergman kernel function on some pseudoconvex domains in Cn, Trans. of A.M.S. 345 (1994), pp. 803-817. | MR | Zbl

[11] D'Angelo (J. P.) .- A Note on the Bergman Kernel, Duke Math. J. 45 (1978), pp. 259-265. | MR | Zbl

[12] D'Angelo (J.P.) .- Real hypersurfaces, orders of contact, and applications, Ann. of Math. 115 (1982), pp. 615-637. | MR | Zbl

[13] D'Angelo (J.P.) .- An explicit computation of the Bergman kernel function, J. Geom. Analysis 4 (1994), pp. 23-34. | MR | Zbl

[14] Diederich (K.) .- Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten, Math. Ann. 187 (1970), pp. 9-36. | MR | Zbl

[15] Diederich (K.) .- Ueber die 1. und 2. Ableitungen der Bergmanschen Kernfunktion und ihr Randverhalten, Math. Ann. 203 (1973), pp. 129-170. | MR | Zbl

[16] Diederich (K.) and Herbort (G.) .- Geometric and analytic boundary invariants. Comparison results, J. Geom. Analysis 3 (1993), pp. 237-267. | MR | Zbl

[17] Diederich (K.) and Herbort (G.) .- Pseudoconvex domains of semiregular type, Contribution to Complex Analysis and Analytic Geometry, Aspects of Mathematics E26, Vieweg 1994. | MR | Zbl

[18] Diederich (K.) and Herbort (G.) .- An alternative proof of a theorem of Boas-Straube-Yu, Complex Analysis and Geometry, Pitman Research notes in Mathematics Series, 366 (1997), pp. 112-118. | MR | Zbl

[19] Diederich (K.), Herbort (G.) and Ohsawa (T.) .- The Bergman kernel on uniformy extendable pseudoconvex domains, Math. Ann. 273 (1986), pp. 471-478. | MR | Zbl

[20] Erdélyi (A.) .- Asymptotic expansions, Dover, New York (1956). | MR | Zbl

[21] Fefferman (C.) . - The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), pp. 1-65. | MR | Zbl

[22] Francsics (G.) and Hanges (N.) .- Explicit formulas for the Szegö kernel on certain weakly pseudoconvex domains, Proc. A.M.S. 123 (1995), pp. 3161-3168. | MR | Zbl

[23] Francsics (G.) and Hanges (N.) .- The Bergman kernel of complex ovals and multivariable hypergeometric functions, to appear in J. Funct. Analysis. | MR | Zbl

[24] Gebelt (N.W.) .- The Bergman kernel on certain weakly pseudoconvex domains, Math. Z. 220 (1995), pp. 1-9. | MR | Zbl

[25] Gong (S.) and Zheng (X.) .- The Bergman kernel function of some Reinhardt domains, Trans. of A.M.S. 348 (1996), pp. 1771-1803. | MR | Zbl

[26] Greiner (P.C.) and Stein (E.M.) .- On the solvability of some differential operators of □b, Proc. Internat. Conf. (Cortona, Italy, 1976-1977), Scuola Norm. Sup. Pisa (1978), pp. 106-165. | MR | Zbl

[27] Haslinger (F.) .- Szegö kernels of certain unbounded domains in C2, Rev. Roumaine Math. Pures Appl. 39 (1994), pp. 939-950. | MR | Zbl

[28] Haslinger (F.) . - Singularities of the Szegö kernels for certain weakly pseudoconvex domains in C2, J. Funct. Analysis 129 (1995), pp. 406-427. | MR | Zbl

[29] Herbort (G.) .- Logarithmic growth of the Bergman kernel for weakly pseudoconvex domains in C3 of finite type, Manuscripta Math. 45 (1983), pp. 69-76. | MR | Zbl

[30] Herbort (G.) . - The growth of the Bergman kernel on pseudoconvex domains of homogeoneous finite diagonal type, Nagoya Math. J. 126 (1992), pp. 1-24. | MR | Zbl

[31] Herbort (G.) .- On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one, Nagoya Math. J. 130 (1993), pp. 25-54. | MR | Zbl

[32] Hörmander (L.) .- L2 estimates and existance theorems for the ∂-operator, Acta Math. 113 (1965), pp. 89-152. | MR | Zbl

[33] Ise (M.) .- On Thullen domains and Hirzebruch manifolds I, J. Math. Soc. Japan 26 (1974), pp. 508-522. | MR | Zbl

[34] Kamimoto (J.) .- Singularities of the Bergman kernel for certain weakly pseudoconvex domains, to appear in the Journal of Math. Sci. the Univ. of Tokyo. | MR | Zbl

[35] Kamimoto (J.) .- On the singularities of non-analytic Szegö kernels, preprint. | MR

[36] Kamimoto (J.) .- On an integral of Hardy and Littlewood, to appear in Kyushu J. of Math. | MR | Zbl

[37] Kamimoto (J.) .- The Bergman kernel on decoupled pseudoconvex domains, to appear in Proc. of I.S.A.A.C. Congress, Reproducing kernels and their applications, Kluwer Academic Publishers. | MR

[38] Kohn (J.J.) .- Boundary behavior of the ∂ on weakly pseudoconvex manifolds of dimension two, J. Diff. Geom. 6 (1972), pp. 523-542. | MR | Zbl

[39] Kohn (J.J.) .- A survey of the ∂-Neumann problem, Proc. Symp. Pure Math. 41 (1984), pp. 137-145. | MR | Zbl

[40] Korányi (A.) . - The Bergman kernel function for tubes over convex cones, Pacific J. Math. 12 (1962), pp. 1355-1359. | MR | Zbl

[41] Krantz (S.G.) .- Geometric Analysis and Function Spaces, C.B.M.S., Amer. Math. Soc. 81. | MR | Zbl

[42] Krantz (S.G.) .- Fatou theorems on domains in Cn, Bull. A.M.S. 16 (1987), pp. 93-96. | MR | Zbl

[43] Krantz (S.G.) .- Invariant metrics and the boundary behavior of holomorphic functions on domains in Cn, J. Geom. Analysis 1 (1991), pp. 71-97. | MR | Zbl

[44] Majima (H.) .- Asymptotic Analysis for Integrable Connections with Irregular Singular Points, Lec. Notes in Math., Springer 1075 (1984). | MR | Zbl

[45] Mcneal (J.D.) .- Local geometry of decoupled pseudoconvex domains, Proceedings in honor of Hans Grauert, Aspekte de Mathematik, Vieweg, Berlin (1990), pp. 223-230. | MR | Zbl

[46] Mcneal (J.D.) .- Estimates on the Bergman kernels of convex domains, Adv. Math. 109 (1994), pp. 108-139. | MR | Zbl

[47] Mcneal (J.D.) .- On large value of L2 Holomorphic functions, Math. Res. Letters 3 (1996), pp. 247-259. | Zbl

[48] Nagel (A.) . - Vector fields and nonisotropic metrics, Beijing Lectures in Harmonic Analysis (E. M. Stein, ed.), Ann. Math. Studies 112, Princeton University Press, Princeton, NXJ, 1986, pp. 241-306. | MR | Zbl

[49] Nagel (A.), Stein (E.M.) and Wainger (S.) .- Boundary behaviorof functions holomorphic in domains of finite type, Natl. Acad. Sci. USA 78 (1981), pp. 6596-6599. | MR | Zbl

[50] Nagel (A.), Stein (E.M.) and Wainger (S.) .- Ball and metrics defined by vector fields I: Basic properties, Acta Math. 155 (1985), pp. 103-147. | MR | Zbl

[51] Nakazawa (N.) .- Asymptotic expansion of the Bergman kernel for strictly pseudoconvex complete Reinhardt domains in C2, Osaka J. Math. 31 (1994), pp. 291-329. | MR | Zbl

[52] Ohsawa (T.) .- Boundary behavior of the Bergman kernel function on pseudoconvex domains, Publ. R.I.M.S., Kyoto Univ. 20 (1984), pp. 897-902. | MR | Zbl

[53] Ohsawa (T.) .- On the extension of L2 holomorphic functions III: negligible weights, Math. Z. 219 (1995), pp. 215-225. | MR | Zbl

[54] Saitoh (S.) .- Fourier-Laplace transforms and the Bergman spaces, Proc. of A.M.S. 102 (1988), pp. 985-992. | MR | Zbl

[55] Sibuya (Y.) . - Perturbation of linear ordinary differential equations at irregular singular points, Funkt. Ekv. 11 (1968), pp. 235-246. | MR | Zbl

[56] Yu (J.) .- Peak functions on weakly pseudoconvex domains, Indiana Univ. Math. J. 43 (1994), pp. 1271-1295. | MR | Zbl