We construct new three-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 / S.G. Krantz, M.M. Peloso, C. Stoppato. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 111:6(2025), pp. e70195.1-e70195.38. [10.1112/jlms.70195]
On a higher dimensional worm domain and its geometric properties
M.M. PelosoPenultimo
;
2025
Abstract
We construct new three-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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