On Hardy spaces on worm domains

Alessandro Monguzzi

Concrete Operators (2016)

  • Volume: 3, Issue: 1, page 29-42
  • ISSN: 2299-3282

Abstract

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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.

How to cite

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Alessandro Monguzzi. "On Hardy spaces on worm domains." Concrete Operators 3.1 (2016): 29-42. <http://eudml.org/doc/277102>.

@article{AlessandroMonguzzi2016,
abstract = {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.},
author = {Alessandro Monguzzi},
journal = {Concrete Operators},
keywords = {Hardy spaces; Szego projection; Worm domains; Szegő projection; worm domains},
language = {eng},
number = {1},
pages = {29-42},
title = {On Hardy spaces on worm domains},
url = {http://eudml.org/doc/277102},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Alessandro Monguzzi
TI - On Hardy spaces on worm domains
JO - Concrete Operators
PY - 2016
VL - 3
IS - 1
SP - 29
EP - 42
AB - 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.
LA - eng
KW - Hardy spaces; Szego projection; Worm domains; Szegő projection; worm domains
UR - http://eudml.org/doc/277102
ER -

References

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