We construct new 3-dimensional variants of the classical Diederich-Fornæss worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
On a higher-dimensional worm domain and its geometric properties / Steven G. Krantz; Marco M. Peloso; Caterina Stoppato. - ELETTRONICO. - (2024).
On a higher-dimensional worm domain and its geometric properties
Caterina Stoppato
2024
Abstract
We construct new 3-dimensional variants of the classical Diederich-Fornæss worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
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