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arXiv · 1910.13741

Holomorphic function spaces on the Hartogs triangle

Alessandro Monguzzi
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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 $L^p$ 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. 2020-12-31. Holomorphic function spaces on the Hartogs triangle. https://arxiv.org/abs/1910.13741

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