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

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- by Michael Christ PDF
- J. Amer. Math. Soc.
**9**(1996), 1171-1185 Request permission

## References

- David E. Barrett,
*Behavior of the Bergman projection on the Diederich-Fornæss worm*, Acta Math.**168**(1992), no. 1-2, 1–10. MR**1149863**, DOI 10.1007/BF02392975 - Steve Bell and Ewa Ligocka,
*A simplification and extension of Fefferman’s theorem on biholomorphic mappings*, Invent. Math.**57**(1980), no. 3, 283–289. MR**568937**, DOI 10.1007/BF01418930 - Harold P. Boas and Emil J. Straube,
*Equivalence of regularity for the Bergman projection and the $\overline \partial$-Neumann operator*, Manuscripta Math.**67**(1990), no. 1, 25–33. MR**1037994**, DOI 10.1007/BF02568420 - Harold P. Boas and Emil J. Straube,
*Sobolev estimates for the $\overline \partial$-Neumann operator on domains in $\textbf {C}^n$ admitting a defining function that is plurisubharmonic on the boundary*, Math. Z.**206**(1991), no. 1, 81–88. MR**1086815**, DOI 10.1007/BF02571327 - David Catlin,
*Subelliptic estimates for the $\overline \partial$-Neumann problem on pseudoconvex domains*, Ann. of Math. (2)**126**(1987), no. 1, 131–191. MR**898054**, DOI 10.2307/1971347 - David W. Catlin,
*Global regularity of the $\bar \partial$-Neumann problem*, Complex analysis of several variables (Madison, Wis., 1982) Proc. Sympos. Pure Math., vol. 41, Amer. Math. Soc., Providence, RI, 1984, pp. 39–49. MR**740870**, DOI 10.1090/pspum/041/740870 - D.-C. Chang, A. Nagel, and E. M. Stein,
*Estimates for the $\overline \partial$-Neumann problem in pseudoconvex domains of finite type in $\textbf {C}^2$*, Acta Math.**169**(1992), no. 3-4, 153–228. MR**1194003**, DOI 10.1007/BF02392760 - M. Christ,
*The Szegö projection need not preserve global analyticity*, Annals of Math.**143**(1996), 301–330. - —,
*Global irregularity for mildly degenerate elliptic operators*, J. Functional Analysis (to appear). - Klas Diederich and John Erik Fornaess,
*Pseudoconvex domains: an example with nontrivial Nebenhülle*, Math. Ann.**225**(1977), no. 3, 275–292. MR**430315**, DOI 10.1007/BF01425243 - John Erik Fornæss and Berit Stensønes,
*Lectures on counterexamples in several complex variables*, Mathematical Notes, vol. 33, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1987. MR**895821** - Tosio Kato,
*Perturbation theory for linear operators*, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR**0203473** - J. J. Kohn,
*Global regularity for $\bar \partial$ on weakly pseudo-convex manifolds*, Trans. Amer. Math. Soc.**181**(1973), 273–292. MR**344703**, DOI 10.1090/S0002-9947-1973-0344703-4 - J. J. Kohn,
*Estimates for $\bar \partial _b$ on pseudoconvex CR manifolds*, Pseudodifferential operators and applications (Notre Dame, Ind., 1984) Proc. Sympos. Pure Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 207–217. MR**812292**, DOI 10.1090/pspum/043/812292

## 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
- MR Author ID: 48950
- Email: christ@math.ucla.edu
- 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 1996 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**9**(1996), 1171-1185 - MSC (1991): Primary 32F20, 35N15
- DOI: https://doi.org/10.1090/S0894-0347-96-00213-5
- MathSciNet review: 1370592