Geodesic
On $L_1$-subspaces of holomorphic functions
Anahit Harutyunyan1 ; Wolfgang Lusky2
1 Faculty of Informatics and Applied Mathematics University of Yerevan Alek Manukian 1 Yerevan 25, Armenia
2 Institute of Mathematics University of Paderborn Warburger Str. 100 D-33098 Paderborn, Germany
Studia Mathematica, Tome 198 (2010) no. 2, pp. 157-175

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study the spaces \[ H_{ \mu}( \Omega) = \bigg\{ f: \Omega \rightarrow \mathbb C \hbox{ holomorphic}:\int_0^R \int_0^{2 \pi} |f(re^{i \varphi})| \,d \varphi \,d \mu(r) \infty \bigg\} \] where $ \Omega$ is a disc with radius $R$ and $ \mu$ is a given probability measure on $[0,R[$. We show that, depending on $ \mu$, $H_{ \mu}( \Omega)$ is either isomorphic to $l_1$ or to $ \left( \sum \oplus A_n \right)_{(1)}$. Here $A_n$ is the space of all polynomials of degree $ \leq n$ endowed with the $L_1$-norm on the unit sphere.
DOI : 10.4064/sm198-2-4
Keywords: study spaces omega bigg omega rightarrow mathbb hbox holomorphic int int varphi varphi infty bigg where omega disc radius given probability measure depending omega either isomorphic sum oplus right here space polynomials degree leq endowed norm unit sphere

Anahit Harutyunyan 1 ; Wolfgang Lusky 2

1 Faculty of Informatics and Applied Mathematics University of Yerevan Alek Manukian 1 Yerevan 25, Armenia
2 Institute of Mathematics University of Paderborn Warburger Str. 100 D-33098 Paderborn, Germany 
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Anahit Harutyunyan; Wolfgang Lusky. On $L_1$-subspaces of holomorphic functions. Studia Mathematica, Tome 198 (2010) no. 2, pp. 157-175. doi: 10.4064/sm198-2-4

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