Boundary behavior of the Bergman kernel function in $\mathbb{C}^2$
Jeffery D. McNeal
Source: Duke Math. J. Volume 58, Number 2
(1989), 499-512.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077307535
Mathematical Reviews number (MathSciNet): MR1016431
Zentralblatt MATH identifier: 0675.32020
Digital Object Identifier: doi:10.1215/S0012-7094-89-05822-5
References
[1] S. R. Bell, Biholomorphic mappings and the $\bar \partial$-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113.
Mathematical Reviews (MathSciNet): MR82j:32039
Zentralblatt MATH: 0423.32009
Digital Object Identifier: doi:10.2307/1971379
JSTOR: links.jstor.org
[2] S. R. Bell, Nonvanishing of the Bergman kernel function at boundary points of certain domains in ${\bf C}\sp{n}$, Math. Ann. 244 (1979), no. 1, 69–74.
Mathematical Reviews (MathSciNet): MR80j:32041
Zentralblatt MATH: 0398.32014
Digital Object Identifier: doi:10.1007/BF01420338
[3] S. Bergman, The kernel function and conformal mapping, American Mathematical Society, Providence, R.I., 1970.
Mathematical Reviews (MathSciNet): MR58:22502
Zentralblatt MATH: 0208.34302
[4] T. Bloom and I. Graham, A geometric characterization of points of type $m$ on real submanifolds of ${\bf C}\sp{n}$, J. Differential Geometry 12 (1977), no. 2, 171–182.
Mathematical Reviews (MathSciNet): MR58:11495
Zentralblatt MATH: 0436.32013
Project Euclid: euclid.jdg/1214433979
[5] D. Catlin, Necessary conditions for subellipticity of the $\bar \partial$-Neumann problem, Ann. of Math. (2) 117 (1983), no. 1, 147–171.
Mathematical Reviews (MathSciNet): MR84c:32021
Zentralblatt MATH: 0552.32017
Digital Object Identifier: doi:10.2307/2006974
JSTOR: links.jstor.org
[6] D. W. Catlin, Global regularity of the $\bar \partial$-Neumann problem, Complex analysis of several variables (Madison, Wis., 1982), Proc. Sympos. Pure Math., vol. 41, Amer. Math. Soc., Providence, RI, 1984, pp. 39–49.
Mathematical Reviews (MathSciNet): MR85j:32033
Zentralblatt MATH: 0578.32031
[7] D. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z., to appear.
Mathematical Reviews (MathSciNet): MR978601
Zentralblatt MATH: 0661.32030
Digital Object Identifier: doi:10.1007/BF01215657
[8] S.-C. Chen, Regularity of the Bergman projection on domains with partial transverse symmetries, Math. Ann. 277 (1987), no. 1, 135–140.
Mathematical Reviews (MathSciNet): MR88e:32034
Zentralblatt MATH: 0603.35067
Digital Object Identifier: doi:10.1007/BF01457283
[9] J. P. D'Angelo, Iterated commutators and derivatives of the Levi form, Complex analysis (University Park, Pa., 1986), Lecture Notes in Math., vol. 1268, Springer, Berlin, 1987, pp. 103–110.
Mathematical Reviews (MathSciNet): MR88k:32050
Zentralblatt MATH: 0647.32011
[10] K. Diederich, Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten, Math. Ann. 187 (1970), 9–36.
Mathematical Reviews (MathSciNet): MR41:7149
Zentralblatt MATH: 0184.31302
Digital Object Identifier: doi:10.1007/BF01368157
[11] K. Diederich, Some recent developments in the theory of the Bergman kernel function: a survey, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 1, Williams Coll., Williamstown, Mass., 1975), Amer. Math. Soc., Providence, R. I., 1977, pp. 127–137.
Mathematical Reviews (MathSciNet): MR56:681
Zentralblatt MATH: 0352.32008
[12] K. Diederich, J. E. Fornaess, and G. Herbort, Boundary behavior of the Bergman metric, Complex analysis of several variables (Madison, Wis., 1982), Proc. Sympos. Pure Math., vol. 41, Amer. Math. Soc., Providence, RI, 1984, pp. 59–67.
Mathematical Reviews (MathSciNet): MR85j:32039
Zentralblatt MATH: 0533.32012
[13] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65.
Mathematical Reviews (MathSciNet): MR50:2562
Zentralblatt MATH: 0289.32012
Digital Object Identifier: doi:10.1007/BF01406845
[14] L. Hörmander, $L\sp{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152.
Mathematical Reviews (MathSciNet): MR31:3691
Zentralblatt MATH: 0158.11002
Digital Object Identifier: doi:10.1007/BF02391775
[15] N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149–158.
Mathematical Reviews (MathSciNet): MR45:3762
Zentralblatt MATH: 0216.10503
Digital Object Identifier: doi:10.1007/BF01419622
[16] J. J. Kohn, Boundary behavior of $\delta$ on weakly pseudo-convex manifolds of dimension two, J. Differential Geometry 6 (1972), 523–542.
Mathematical Reviews (MathSciNet): MR48:727
Zentralblatt MATH: 0256.35060
Project Euclid: euclid.jdg/1214430641
[17] J. J. Kohn, Pseudo-differential operators and non-elliptic problems, Pseudo-Diff. Operators (C.I.M.E., Stresa, 1968), Edizioni Cremonese, Rome, 1969, pp. 157–165.
Mathematical Reviews (MathSciNet): MR41:3972
[18] J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492.
Mathematical Reviews (MathSciNet): MR31:6041
Zentralblatt MATH: 0125.33302
Digital Object Identifier: doi:10.1002/cpa.3160180305
[19] A. Nagel, E. M. Stein, and S. Wainger, Balls and metrics defined by vector fields. I. Basic properties, Acta Math. 155 (1985), no. 1-2, 103–147.
Mathematical Reviews (MathSciNet): MR86k:46049
Zentralblatt MATH: 0578.32044
Digital Object Identifier: doi:10.1007/BF02392539
[20] A. Nagel, J. P. Rosay, E. M. Stein, and S. Wainger, Estimates for the Bergman and Szegö kernels in $\mathbb{C}^2$, preprint.
Mathematical Reviews (MathSciNet): MR979602
Digital Object Identifier: doi:10.2307/1971487
JSTOR: links.jstor.org
[21] S. M. Webster, Biholomorphic mappings and the Bergman kernel off the diagonal, Invent. Math. 51 (1979), no. 2, 155–169.
Mathematical Reviews (MathSciNet): MR81e:32029
Zentralblatt MATH: 0385.32019
Digital Object Identifier: doi:10.1007/BF01390226
[22] C. L. Fefferman and J. J. Kohn, Hölder estimates on domains of complex dimension two and on three-dimensional CR manifolds, Adv. in Math. 69 (1988), no. 2, 223–303.
Mathematical Reviews (MathSciNet): MR89g:32027
Zentralblatt MATH: 0649.35068
Digital Object Identifier: doi:10.1016/0001-8708(88)90002-3
[23] M. Christ, Regularity properties of the $\bar \partial_b$ equation on weakly pseudo-convex CR manifolds of dimension $3$, preprint.
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