The definition of classical holomorphic function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of holomorphic function spaces on the Hartogs triangle which includes some weighted Bergman spaces, a candidate Hardy space and a candidate Dirichlet space. For the weighted Bergman spaces and the Hardy space we study the (Formula presented.) mapping properties of Bergman and Szegő projection respectively, whereas for the Dirichlet space we prove it is isometric to the Dirichlet space on the bidisc.
(2021). Holomorphic function spaces on the Hartogs triangle [journal article - articolo]. In MATHEMATISCHE NACHRICHTEN. Retrieved from http://hdl.handle.net/10446/200828
Holomorphic function spaces on the Hartogs triangle
Monguzzi, Alessandro
2021-01-01
Abstract
The definition of classical holomorphic function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of holomorphic function spaces on the Hartogs triangle which includes some weighted Bergman spaces, a candidate Hardy space and a candidate Dirichlet space. For the weighted Bergman spaces and the Hardy space we study the (Formula presented.) mapping properties of Bergman and Szegő projection respectively, whereas for the Dirichlet space we prove it is isometric to the Dirichlet space on the bidisc.| File | Dimensione del file | Formato | |
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2021 - Monguzzi - Holomorphic function spaces on the Hartogs triangle.pdf
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1910.13741.pdf
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Descrizione: "This is the peer reviewed version of the following article: Monguzzi, A. Holomorphic function spaces on the Hartogs triangle. Mathematische Nachrichten. 2021; 294: 2209– 2231, which has been published in final form at 10.1002/mana.201900477. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited."
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