Remarks on the Bergman kernel function of a worm domain

 Access to full text

 Full (PDF)

1. [1] D. E. Barrett, Behavior of the Bergman projection on the Diederich-Fornæss worm, Acta Math. 168 (1992), 1-10. Zbl0779.32013
2. [2] S. Bell, A duality theorem for harmonic functions, Michigan Math. J. 29 (1982), 123-128. Zbl0482.31004
3. [3] S. Bell and H. Boas, Regularity of the Bergman projections in weakly pseudoconvex domains, Math. Ann. 257 (1981), 23-30. Zbl0451.32017
4. [4] S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283-285. Zbl0411.32010
5. [5] H. Boas and E. Straube, Equivalence of regularity for the Bergman projection and the $\overline{\partial }$- Neumann operator, Manuscripta Math. 67 (1990), 25-33. Zbl0695.32011
6. [6] M. Christ, Global $C^{\infty }$ irregularity of the $\overline{\partial }$- Neumann problem for worm domains, J. Amer, Math. Soc. 9 (1996), 1171-1185. Zbl0945.32022
7. [7] K. Diederich and J. E. Fornæss, Pseudoconvex domains: an example with non-trivial Nebenhülle, Math. Ann. (1977), 275-292. Zbl0327.32008
8. [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. Zbl0247.35093
9. [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. Zbl0744.32011
10. [10] J. J. Kohn, Global regularity for $\overline{\partial }$ on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292 Zbl0276.35071
11. [11] E. Ligocka, Some remarks on extension of biholomorphic mappings, in: Analytic Functions (Kozubnik, 1979), Lecture Notes in Math. 798, Springer, 1980, 350-363. 
12. [12] S. Webster, Biholomorphic mappings and the Bergman kernel off diagonal, Invent. Math. 51 (1979), 155-169. Zbl0385.32019