On L₁-subspaces of holomorphic functions

Anahit Harutyunyan; Wolfgang Lusky

Studia Mathematica, Tome 196 (2010), p. 157-175 / Harvested from The Polish Digital Mathematics Library

Résumé

We study the spaces $H_{μ} (Ω) = f : Ω \to ℂ h o l o m o r p h i c : \int_{0}^{R} \int_{0}^{2 π} | f (r e^{i φ}) | d φ d μ (r) < \infty$ where Ω is a disc with radius R and μ is a given probability measure on [0,R[. We show that, depending on μ, $H_{μ} (Ω)$ is either isomorphic to l₁ or to ${(\sum \oplus A ₙ)}_{(1)}$ . Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.

Publié le : 2010-01-01

Zbl 1201.46026

EUDML-ID : urn:eudml:doc:285697

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     title = {On L1-subspaces of holomorphic functions},
     journal = {Studia Mathematica},
     volume = {196},
     year = {2010},
     pages = {157-175},
     zbl = {1201.46026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-4}
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Anahit Harutyunyan; Wolfgang Lusky. On L₁-subspaces of holomorphic functions. Studia Mathematica, Tome 196 (2010) pp. 157-175. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-4/