In this review article we present the problem of studying Hardy spaces and the related Szego projection on worm domains. We review the importance of the Diederich-Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szego projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth worm domains.
Monguzzi, A. (2016). On Hardy spaces on worm domains. CONCRETE OPERATORS, 3(1), 29-42 [10.1515/conop-2016-0005].
On Hardy spaces on worm domains
MONGUZZI, ALESSANDRO
2016
Abstract
In this review article we present the problem of studying Hardy spaces and the related Szego projection on worm domains. We review the importance of the Diederich-Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szego projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth worm domains.
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