On Hardy spaces on worm domains
In this review article we present the problem of studying Hardy spaces and the related Szeg˝o 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 hi...
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-04-01
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| Series: | Concrete Operators |
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| Online Access: | http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0005/conop-2016-0005.xml?format=INT |
| Summary: | In this review article we present the problem of studying Hardy spaces and the related Szeg˝o 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 Szeg˝o 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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| ISSN: | 2299-3282 |