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 |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0005/conop-2016-0005.xml?format=INT |
| _version_ | 1819110335454380032 |
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| author | Monguzzi Alessandro |
| author_facet | Monguzzi Alessandro |
| author_sort | Monguzzi Alessandro |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T03:40:05Z |
| format | Article |
| id | doaj.art-c8ba6061d8014e24916ccdcf21dbcb12 |
| institution | Directory Open Access Journal |
| issn | 2299-3282 |
| language | English |
| last_indexed | 2024-12-22T03:40:05Z |
| publishDate | 2016-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Concrete Operators |
| spelling | doaj.art-c8ba6061d8014e24916ccdcf21dbcb122022-12-21T18:40:17ZengDe GruyterConcrete Operators2299-32822016-04-0131294210.1515/conop-2016-0005conop-2016-0005On Hardy spaces on worm domainsMonguzzi Alessandro0Dipartimento di Matematica, Università degli Studi di Milano, via C. Saldini 50, 20133, Milano, ItalyIn 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.http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0005/conop-2016-0005.xml?format=INTHardy spaces Szego projection Worm domains |
| spellingShingle | Monguzzi Alessandro On Hardy spaces on worm domains Concrete Operators Hardy spaces Szego projection Worm domains |
| title | On Hardy spaces on worm domains |
| title_full | On Hardy spaces on worm domains |
| title_fullStr | On Hardy spaces on worm domains |
| title_full_unstemmed | On Hardy spaces on worm domains |
| title_short | On Hardy spaces on worm domains |
| title_sort | on hardy spaces on worm domains |
| topic | Hardy spaces Szego projection Worm domains |
| url | http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0005/conop-2016-0005.xml?format=INT |
| work_keys_str_mv | AT monguzzialessandro onhardyspacesonwormdomains |