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.

Monguzzi, A. (2021). Holomorphic function spaces on the Hartogs triangle. MATHEMATISCHE NACHRICHTEN, 294(11), 2209-2231 [10.1002/mana.201900477].

Holomorphic function spaces on the Hartogs triangle

Monguzzi A.
2021

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.
Articolo in rivista - Articolo scientifico
Bergman projection; Dirichlet space; Hardy space; Hartogs triangle
English
2209
2231
23
Green Open Access
Monguzzi, A. (2021). Holomorphic function spaces on the Hartogs triangle. MATHEMATISCHE NACHRICHTEN, 294(11), 2209-2231 [10.1002/mana.201900477].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/343055
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