We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be -smoothly extended to the boundary.
@article{bwmeta1.element.bwnjournal-article-smv130i2p109bwm, author = {Ewa Ligocka}, title = {Remarks on the Bergman kernel function of a worm domain}, journal = {Studia Mathematica}, volume = {129}, year = {1998}, pages = {109-113}, zbl = {0907.32008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv130i2p109bwm} }
Ligocka, Ewa. Remarks on the Bergman kernel function of a worm domain. Studia Mathematica, Tome 129 (1998) pp. 109-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i2p109bwm/
[00000] [1] D. E. Barrett, Behavior of the Bergman projection on the Diederich-Fornæss worm, Acta Math. 168 (1992), 1-10. | Zbl 0779.32013
[00001] [2] S. Bell, A duality theorem for harmonic functions, Michigan Math. J. 29 (1982), 123-128. | Zbl 0482.31004
[00002] [3] S. Bell and H. Boas, Regularity of the Bergman projections in weakly pseudoconvex domains, Math. Ann. 257 (1981), 23-30. | Zbl 0451.32017
[00003] [4] S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283-285. | Zbl 0411.32010
[00004] [5] H. Boas and E. Straube, Equivalence of regularity for the Bergman projection and the - Neumann operator, Manuscripta Math. 67 (1990), 25-33. | Zbl 0695.32011
[00005] [6] M. Christ, Global irregularity of the - Neumann problem for worm domains, J. Amer, Math. Soc. 9 (1996), 1171-1185. | Zbl 0945.32022
[00006] [7] K. Diederich and J. E. Fornæss, Pseudoconvex domains: an example with non-trivial Nebenhülle, Math. Ann. (1977), 275-292. | Zbl 0327.32008
[00007] [8] G. B. Folland and J. J. Kohn, The Neumann Problem for the Cauchy - Riemann Complex, Ann. of Math. Stud. 72, Princeton Univ. Press, 1972. | Zbl 0247.35093
[00008] [9] C. O. Kiselman, A study of the Bergman projection in certain Hartogs domains, in: Proc. Sympos. Pure Math. 52, Part 3, Amer, Math. Soc., 1991, 219-231. | Zbl 0744.32011
[00009] [10] J. J. Kohn, Global regularity for on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292 | Zbl 0276.35071
[00010] [11] E. Ligocka, Some remarks on extension of biholomorphic mappings, in: Analytic Functions (Kozubnik, 1979), Lecture Notes in Math. 798, Springer, 1980, 350-363.
[00011] [12] S. Webster, Biholomorphic mappings and the Bergman kernel off diagonal, Invent. Math. 51 (1979), 155-169. | Zbl 0385.32019