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Holomorphic function spaces on the Hartogs triangle

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  • Alessandro Monguzzi

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 Lp 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.

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  • Alessandro Monguzzi, 2021. "Holomorphic function spaces on the Hartogs triangle," Mathematische Nachrichten, Wiley Blackwell, vol. 294(11), pages 2209-2231, November.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:11:p:2209-2231
    DOI: 10.1002/mana.201900477
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