Holomorphic reproducing kernels in Reinhardt domains.



Pacific Journal of Mathematics

Holomorphic reproducing kernels in Reinhardt domains.

Harold P. Boas

Source: Pacific J. Math. Volume 112, Number 2 (1984), 273-292.

Primary Subjects: 32H10
Secondary Subjects: 46E20

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102709605
Zentralblatt MATH identifier: 0532.32011
Zentralblatt MATH identifier: 0497.32021
Mathematical Reviews number (MathSciNet): MR743985

References

[I] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404.
Mathematical Reviews (MathSciNet): MR14:479c
Zentralblatt MATH: 0037.20701
[2] D. Barrett, Regularity of the Bergman projection on domains with transverse symme- tries, Math. Ann., 258 (1982), 441-446.
Mathematical Reviews (MathSciNet): MR83i:32032
Zentralblatt MATH: 0486.32015
[3] S. R. Bell, Biholomorphic mappings and the d-problem, Annals of Math., 114 (1981), 103-113.
Mathematical Reviews (MathSciNet): MR82j:32039
Zentralblatt MATH: 0423.32009
[4] S. R. Bell, A representation theorem in strictly pseudoconvex domains, Illinois J. Math., 26 (1982), 19-26.
Mathematical Reviews (MathSciNet): MR83c:32036
Zentralblatt MATH: 0475.32004
[5] S. R. Bell and H. P. Boas, Regularity of the Bergman projection in weakly pseudocon- vex domains, Math. Ann., 257 (1981), 23-30.
Mathematical Reviews (MathSciNet): MR83b:32021
Zentralblatt MATH: 0451.32017
[6] S. R. Bell and D. Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J., 49 (1982), 385-396.
Mathematical Reviews (MathSciNet): MR84b:32037a
Zentralblatt MATH: 0475.32011
[7] J. Bergh and J. Lfstrm, Interpolation Spaces, Springer-Verlag, 1976.
Mathematical Reviews (MathSciNet): MR58:2349
Zentralblatt MATH: 0344.46071
[8] S. Bergman, The Kernel Function and Conformal Mapping, 2nd ed., Providence: Amer. Math. Soc, 1970.
Mathematical Reviews (MathSciNet): MR58:22502
Zentralblatt MATH: 0040.19001
[9] D. Catlin, Boundary behavior of holomorphic functions on pseudoconvex domains, J. Differential Geometry, 15 (1980), 605-625.
Mathematical Reviews (MathSciNet): MR83b:32013
Zentralblatt MATH: 0484.32005
[10] D. Catlin, personal communication.
[II] H. G. Eggleston, Convexity, Cambridge University Press, 1958.
Mathematical Reviews (MathSciNet): MR23:A2123
[12] 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
[13] S. Karlin, Total Positivity, Stanford: Stanford University Press, 1968.
Mathematical Reviews (MathSciNet): MR37:5667
Zentralblatt MATH: 0219.47030
[14] J. J. Kohn, Global regularity of d on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc, 181 (1973), 273-292.
Mathematical Reviews (MathSciNet): MR49:9442
Zentralblatt MATH: 0276.35071
[15] S. Krantz, Function Theory of Several Complex Variables,New York: Wiley, 1982.
Mathematical Reviews (MathSciNet): MR84c:32001
Zentralblatt MATH: 0471.32008
[16] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. L, Springer-Verlag, 1972.
Zentralblatt MATH: 0227.35001
[17] A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and its Applica- tions, New York: Academic Press, 1979.
Mathematical Reviews (MathSciNet): MR81b:00002
Zentralblatt MATH: 0437.26007

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