Available in electronic format
Available in print format		 Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN: 1088-6834(e) ISSN: 0894-0347(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Global $C^{\infty }$ irregularity of the $\bar \partial $--Neumann problem for worm domains

Author(s): Michael Christ
Journal: J. Amer. Math. Soc. 9 (1996), 1171-1185.
MSC (1991): Primary 32F20, 35N15
Retrieve article in: PDF DVI PostScript
This article is available free of charge

References | Similar articles | Additional information

References:

[B]
D. Barrett, Behavior of the Bergman projection on the Diederich-Fornæss worm, Acta Math. 168 (1992), 1--10. MR 93c:32033

[BL]
S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorems on biholomorphic mappings, Invent. Math. 57 (1980), 283--289. MR 81i:32017

[BS1]
H. Boas and E. Straube, Equivalence of regularity for the Bergman projection and the $\bar \partial $--Neumann operator, Manuscripta Math. 67 (1990), 25--33. MR 90k:32057

[BS2]
------, Sobolev estimates for the $\bar \partial $--Neumann operator on domains in $\mathbf {C}^{n}$ admitting a defining function that is plurisubharmonic on the boundary, Math. Zeitschrift 206 (1991), 81--88. MR 92b:32027

[Ca1]
D. Catlin, Subelliptic estimates for the $\bar \partial $--Neumann problem on pseudoconvex domains, Annals of Math. 126 (1987), 131--191. MR 88i:32025

[Ca2]
------, Global regularity of the $\bar \partial $--Neumann problem, Proc. Symp. Pure Math. 41 (1984), 39--49. MR 85j:32033

[CNS]
D.-C. Chang, A. Nagel and E. M. Stein, Estimates for the $\bar \partial $--Neumann problem in pseudoconvex domains of finite type in $\mathbf C ^{2}$, Acta Math. 169 (1992), 153-228. MR 93k:32025

[Ch1]
M. Christ, The Szegö projection need not preserve global analyticity, Annals of Math. 143 (1996), 301--330.

[Ch2]
------, Global irregularity for mildly degenerate elliptic operators, J. Functional Analysis (to appear).

[DF]
K. Diederich and J. E. Fornæss, Pseudoconvex domains: an example with nontrivial Nebenhülle, Math. Ann. 225 (1977), 275--292. MR 55:3320

[FS]
J. E. Fornæss and B. Stensønes, Lectures On Counterexamples In Several Complex Variables, Mathematical Notes 33, Princeton University Press, Princeton, NJ, 1987. MR 88f:32001

[Ka]
T. Kato, Perturbation Theory For Linear Operators, Springer-Verlag, New York, 1966. MR 34:3324

[K1]
J. J. Kohn, Global regularity for $\bar \partial $ on weakly pseudoconvex manifolds, Trans. AMS 181 (1973), 273--292. MR 49:9442

[K2]
------, Estimates for $\bar \partial _{b}$ on pseudoconvex CR manifolds, Proc. Symp. Pure Math. 43 (1985), 207--217. MR 87c:32025

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 32F20, 35N15

Retrieve articles in all Journals with MSC (1991): 32F20, 35N15

Additional Information:

Michael Christ
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Address at time of publication: Department of Mathematics, University of California, Berkeley, California 94720
Email: christ@math.ucla.edu

DOI: 10.1090/S0894-0347-96-00213-5
PII: S 0894-0347(96)00213-5
Received by editor(s): August 15, 1995
Received by editor(s) in revised form: December 27, 1995
Additional Notes: Research supported by National Science Foundation grant DMS-9306833. I am indebted to D. Barrett, E. Straube, J. J. Kohn, P. Matheos and J. McNeal for stimulating conversations and useful comments on the exposition.
Copyright of article: Copyright 1996, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google