Precise regularity up to the boundary of proper holomorphic mappings

Bernard Coupet

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1993)

  • Volume: 20, Issue: 3, page 461-482
  • ISSN: 0391-173X

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Coupet, Bernard. "Precise regularity up to the boundary of proper holomorphic mappings." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 20.3 (1993): 461-482. <http://eudml.org/doc/84157>.

@article{Coupet1993,
author = {Coupet, Bernard},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {regularity up to the boundary; strictly pseudoconvex domains; proper holomorphic mapping},
language = {eng},
number = {3},
pages = {461-482},
publisher = {Scuola normale superiore},
title = {Precise regularity up to the boundary of proper holomorphic mappings},
url = {http://eudml.org/doc/84157},
volume = {20},
year = {1993},
}

TY - JOUR
AU - Coupet, Bernard
TI - Precise regularity up to the boundary of proper holomorphic mappings
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1993
PB - Scuola normale superiore
VL - 20
IS - 3
SP - 461
EP - 482
LA - eng
KW - regularity up to the boundary; strictly pseudoconvex domains; proper holomorphic mapping
UR - http://eudml.org/doc/84157
ER -

References

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  1. [Al] H. Alexander, Proper holomorphic mappings in Cn. Indiana Univ. Math. J.26 (1977), 137-146. Zbl0391.32015MR422699
  2. [Al-Ba-Ro] S. Alinhac - M.S. Baouendi - L. Rothchild, Unique continuation and regularity at the boundary for holomorphic functions. To appear. Zbl0718.32021
  3. [Be-Li] S. Bell - E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings. Invent. Math.57 (1980), 283-289. Zbl0411.32010MR568937
  4. [Co1] B. Coupet, Régularité de fonctions holomorphes sur des sous-variétés totalement réelles maximales. Structure des espaces de Bergman. Thèse d'état (1987), Marseille. 
  5. [Co2] B. Coupet, Régularité de fonctions holomorphes sur des wedges. Canad. J. Math. XL3 (1988), 532-545. Zbl0687.32009MR960595
  6. [Co3] B. Coupet, Construction de disques analytiques et régularité de fonctions holomorphes au bord. Math. Z.209 (1992), 179-204. Zbl0787.32028MR1147813
  7. [Er] B. Errike, The relation between the solid modulus of continuity and the modulus of continuity along the Shilov boundaries for analytic functions of several variables. Math. USSR-Sb.50 (1985), 495-511. Zbl0573.32009
  8. [Fe] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26 (1974), 1-65. Zbl0289.32012MR350069
  9. [Fo-Lo] J.E. Fornaess - E. Low, Proper holomorphic mappings. Math. Scand.58 (1986), 311-322. Zbl0618.32022MR860886
  10. [Fo] F. Forstneric, Proper holomorphic mappings: A survey. Preprint Series Dept. Math. Univ. E.T. Lubjana. MR1207867
  11. [Gi-Tr] D. Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer Verlag1977. Zbl0361.35003MR473443
  12. [Gr] I. Graham, Boundary behavior of the Caratheodory and Kobayashi metrics on strongly pseudoconvex domains in Cn with smooth boundary. Trans. Amer. Math. Soc.207 (1975), 219-240. Zbl0305.32011MR372252
  13. [Ha] S.V. Hasanov, Correspondence of boundaries under biholomorphic maps in Cn. Sib. Math. J.29 (1989), 462-467. Zbl0666.32014
  14. [Ha-Pi] S.V. Hasanov - S. Pinchuk, Asymptotically holomorphic functions and their applications. Math. USSR-Sb.62 (1989), 541-550. Zbl0663.32006MR933702
  15. [He] G.M. Henkin, An analytic polyedron is not holomorphically equivalent to a strictly pseudoconvex domain. Soviet Math. Dokl.14 (1973), 858-862. Zbl0288.32015MR328125
  16. [Kr] S.G. Krantz, Function Theory of Several Complex Variables. Wiley-Interscience, Pure and Appl. Math. Series, 1982. Zbl0471.32008MR635928
  17. [Le] L. Lempert, A precise result on the boundary regularity of biholomorphic mappings. Math. Z.193 (1986), 559-579. Zbl0603.32013MR867348
  18. [Li] E. Ligocka, The Hölder continuity of the Bergman projection and proper holomorphic mappings. Studia Math.80 (1984), 89-107. Zbl0566.32017MR781328
  19. [Lw] H. Lewy, On the boundary behavior of holomorphic mappings. Acad. Waz. Linei35 (1977), 1-8. 
  20. [Ni-We-Ya] L. Nirenberg - S. Webster - P. Yang, Local boundary regularity of holomorphic mappings. Comm. Pure Appl. Math.33 (1980), 305-328. Zbl0436.32018MR562738
  21. [Pi1] S. Pinchuk, On the analytic continuation of biholomorphic mappings. Math. USSR-Sb.27 (1975), 375-392. Zbl0366.32010
  22. [Pi2] S. Pinchuk, Holomorphic inequivalence of some classes of domain in Cn. Math. USSR-Sb.39 (1981), 61-86. Zbl0464.32014
  23. [Pi3] S. Pinchuk, The scaling method and holomorphic mappings. AMS Summer Research Institute on several complex variables and complex geometry, Santa-Cruz, California, July 1989. Zbl0744.32013
  24. [Ra] R.M. Range, Holomorphic Functions and Integral Representation in Several Complex Variables. Springer-Verlag. Zbl0591.32002MR847923
  25. [Ro] J.P. Rosay, A propos de "wedges" et d' "edges" et de prolongements holomorphes. Trans. Amer. Math. Soc.29 (1986), 63-72. Zbl0629.32009MR849467
  26. [Ru1] W. Rudin, Function Theory in Polydiscs. W.A. Benjamin Inc., 1969. Zbl0177.34101MR255841
  27. [Ru2] W. Rudin, Function Theory on the Unit Ball of Cn. Springer, New-York, 1980. Zbl0495.32001MR601594
  28. [Si] N. Sibony, A class of hyperbolic manifolds in Recent Developments in Several Complex Variables, J.E. Fornaess ed., Annals of Mathematics Studies, Princeton University Press, 1981. Zbl0476.32033MR627768
  29. [St] E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton1970. Zbl0207.13501MR290095
  30. [Str] E. Straube, Interpolation between Sobolev and between Lipschitz spaces of analytic functions on starshaped domains. Trans. Amer. Math. Soc.316 (1989), 653-671. Zbl0695.46034MR943308
  31. [We] S. Webster, On the reflection principle in several complex variables. Proc. Amer. Math. Soc.71 (1978), 26-28. Zbl0626.32019MR477138

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