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Transactions of the American Mathematical Society

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Local Boundary Regularity
of the Szego Projection
and Biholomorphic Mappings
of Non-Pseudoconvex Domains


Author: Peiming Ma
Journal: Trans. Amer. Math. Soc. 350 (1998), 419-428
MSC (1991): Primary 32H10
DOI: https://doi.org/10.1090/S0002-9947-98-01908-4
MathSciNet review: 1407706
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the Szeg\H{o} projection $S$ of a smoothly bounded domain $\Omega $, not necessarily pseudoconvex, satisfies local regularity estimates at certain boundary points, provided that condition $R$ holds for $\Omega $. It is also shown that any biholomorphic mapping $f:\Omega \rightarrow D$ between smoothly bounded domains extends smoothly near such points, provided that a weak regularity assumption holds for $D$.


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  • 1. D. Barrett, Irregularity of the Bergman projection on a smooth bounded domain in $\mathbb{C}^{2}$, Ann. Math. 119 (1984), 431-436. MR 85e:32030
  • 2. -, Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann. 258 (1982), 441-446. MR 83i:32032
  • 3. D. Barrett and J. Fornæss, Uniform approximation of holomorphic functions on bounded Hartogs domains in $\mathbb{C}^{2}$, Math. Z. 191 (1986), 61-72. MR 82e:32022
  • 4. S. Bell, Differentiability of the Bergman kernel and pseudo-local estimates, Math. Z. 192 (1986), 467-472. MR 87i:32034
  • 5. -, Local boundary behavior of proper holomorphic mappings, Proc. Sympos. Pure Math., vol. 41, A.M.S., Providence, 1984, pp. 1-7. MR 85j:32043
  • 6. -, Boundary behavior of proper holomorphic mappings between non-pseudoconvex domains, Am. J. of Math. 106 (1984), 639-643. MR 86a:32054
  • 7. S. Bell and H. Boas, Regularity of the Bergman projection in weakly pseudoconvex domains, Math. Ann. 257 (1981), 23-30. MR 83b:32021
  • 8. S. Bell and D. Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J. 49 (1982), 385-396. MR 84b:32037a
  • 9. S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283-289. MR 81i:32017
  • 10. H. Boas, The Szego projection: Sobolev estimates in regular domains, Trans. Amer. Math. Soc. 300 (1987), 109-132. MR 88d:32030
  • 11. -, Extension of Kerzman's theorem on differentiability of the Bergman kernel function, Indiana Univ. Math. Journal 36 (1987), 495-499. MR 88j:32028
  • 12. -, Sobolev space projections in strictly pseudoconvex domains, Trans. Amer. Math. Soc. 288 (1985), 227-240. MR 86g:32041
  • 13. D. Catlin, Subelliptic estimates for the $\bar \partial $-Neumann problem on pseudoconvex domains, Ann. Math. 126 (1987), 131-191. MR 88i:32025
  • 14. J. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. Math. 115 (1982), 615-637. MR 84a:32027
  • 15. K. Diederich and J. E. Fornæss, Boundary regularity of proper holomorphic mappings, Invent. Math. 67 (1982), 363-384. MR 84b:32037b
  • 16. -, Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), 129-141. MR 55:10728
  • 17. F. Forstneric and J-P. Rosay, Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings, Math. Ann. 279 (1987), 239-252. MR 89c:32070
  • 18. J. J. Kohn, A survey of the $\bar \partial $-Neumann problem, Proc. Sympos. Pure Math. 41, A.M.S., Providence, 1984, pp. 137-145. MR 85e:32023
  • 19. L. Lempert, On the boundary behavior of holomorphic mappings, Contributions to Several Complex Variables (A. Howard and P.-M. Wong, editors), Vieweg, Braunschweig, 1986, pp. 193-215. MR 87m:32058
  • 20. P. Ma, Local boundary regularity of the Bergman projection in non-pseudoconvex domains, Ill. J. of Math. 37 (1993), 49-68. MR 93k:32048
  • 21. E. Straube, Harmonic and analytic functions admitting a distribution boundary value, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), 559-586. MR 87c:31006

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Additional Information

Peiming Ma
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Wisconsin-Stout, Menomonie, Wisconsin 54751
Email: map@uwstout.edu

DOI: https://doi.org/10.1090/S0002-9947-98-01908-4
Received by editor(s): September 25, 1995
Received by editor(s) in revised form: July 30, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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