Data di Pubblicazione:
2023
Citazione:
Irregularity of the Bergman Projection on Smooth Unbounded Worm Domains / S.G. Krantz, A. Monguzzi, M.M. Peloso, C. Stoppato. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - 20:3(2023), pp. 128.1-128.19. [10.1007/s00009-023-02331-3]
Abstract:
In this work, we consider smooth unbounded worm domains Zλ in C2 and show that the Bergman projection, densely defined on the Sobolev spaces Hs,p(Zλ) , p∈ (1 , ∞) , s≥ 0 , does not extend to a bounded operator Pλ: Hs,p(Zλ) → Hs,p(Zλ) when s> 0 or p≠ 2. The same irregularity was known in the case of the non-smooth unbounded worm. This improved result shows that the irregularity of the projection is not a consequence of the irregularity of the boundary but instead of the infinite windings of the worm domain.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Bergman kernel; Bergman projection; worm domain
Elenco autori:
S.G. Krantz, A. Monguzzi, M.M. Peloso, C. Stoppato
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