## Duke Mathematical Journal

### Regularity of the Bergman projection and local geometry of domains

David E. Barrett

#### Article information

Source
Duke Math. J. Volume 53, Number 2 (1986), 333-343.

Dates
First available in Project Euclid: 20 February 2004

http://projecteuclid.org/euclid.dmj/1077305046

Digital Object Identifier
doi:10.1215/S0012-7094-86-05321-4

Mathematical Reviews number (MathSciNet)
MR850539

Zentralblatt MATH identifier
0615.32016

Subjects
Primary: 32H10
Secondary: 32H35: Proper mappings, finiteness theorems

#### Citation

Barrett, David E. Regularity of the Bergman projection and local geometry of domains. Duke Math. J. 53 (1986), no. 2, 333--343. doi:10.1215/S0012-7094-86-05321-4. http://projecteuclid.org/euclid.dmj/1077305046.

#### References

• [1] D. Barrett, Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann. 258 (1981/82), no. 4, 441–446.
• [2] D. Barrett, Irregularity of the Bergman projection on a smooth bounded domain in $\bf C\sp2$, Ann. of Math. (2) 119 (1984), no. 2, 431–436.
• [3] S. Bell, Biholomorphic mappings and the $\bar \partial$-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113.
• [4] S. Bell, Analytic hypoellipticity of the $\bar \partial$-Neumann problem and extendability of holomorphic mappings, Acta Math. 147 (1981), no. 1-2, 109–116.
• [5] S. Bell, Regularity of the Bergman projection in certain nonpseudoconvex domains, Pacific J. Math. 105 (1983), no. 2, 273–277.
• [6] H. Boas, Holomorphic reproducing kernels in Reinhardt domains, Pacific J. Math. 112 (1984), no. 2, 273–292.
• [7] D. Catlin, Global regularity of the $\bar \partial$-Neumann problem, Complex analysis of several variables (Madison, Wis., 1982), Proc. Symp. Pure Math., vol. 41, Amer. Math. Soc., Providence, RI, 1984, pp. 39–49.
• [8] D. Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. (2) 120 (1984), no. 3, 529–586.
• [9] B. Dahlberg, Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain, Studia Math. 67 (1980), no. 3, 297–314.
• [10] J. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), no. 3, 615–637.
• [11] K. Diederich and J. E. Fornaess, Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), no. 2, 129–141.
• [12] G. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, vol. 75, Princeton University Press, Princeton, N.J., 1972.
• [13] D. Jerison and C. Kenig, Boundary value problems on Lipschitz domains, Studies in partial differential equations, MAA Studies in Mathematics, vol. 23, Math. Assoc. America, Washington, DC, 1982, pp. 1–68.
• [14] J. J. Kohn, Subellipticity of the $\bar \partial$-Neumann problem on pseudo-convex domains: sufficient conditions, Acta Math. 142 (1979), no. 1-2, 79–122.
• [15] J. J. Kohn, personal communication.
• [16] G. Komatsu and S. Ozawa, Variation of the Bergman kernel by cutting a hole, preprint.
• [17] L. Lempert, On the boundary behavior of holomorphic mappings, preprint.
• [18] J. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Die Grundlehren der mathematischen Wissenschaften, vol. 181, Springer-Verlag, New York, 1972.
• [19] R. M. Range, The Caratheodory metric and holomorphic maps on a class of weakly pseudoconvex domains, Pacific J. Math. 78 (1978), no. 1, 173–189.
• [20] E. Straube, Harmonic and analytic functions admitting a distribution boundary value, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 4, 559–591.