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We study the spaces
where Ω is a disc with radius R and μ is a given probability measure on [0,R[. We show that, depending on μ, is either isomorphic to l₁ or to . Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.
Anahit Harutyunyan, and Wolfgang Lusky. "On L₁-subspaces of holomorphic functions." Studia Mathematica 198.2 (2010): 157-175. <http://eudml.org/doc/285697>.
@article{AnahitHarutyunyan2010, abstract = {We study the spaces
$H_\{μ\}(Ω) = \{f: Ω → ℂ holomorphic: ∫_\{0\}^\{R\} ∫_\{0\}^\{2π\} |f(re^\{iφ\})| dφdμ(r) < ∞\}$
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 $(∑ ⊕ Aₙ)_\{(1)\}$. Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.}, author = {Anahit Harutyunyan, Wolfgang Lusky}, journal = {Studia Mathematica}, keywords = {Hardy space; isomorphism}, language = {eng}, number = {2}, pages = {157-175}, title = {On L₁-subspaces of holomorphic functions}, url = {http://eudml.org/doc/285697}, volume = {198}, year = {2010}, }
TY - JOUR AU - Anahit Harutyunyan AU - Wolfgang Lusky TI - On L₁-subspaces of holomorphic functions JO - Studia Mathematica PY - 2010 VL - 198 IS - 2 SP - 157 EP - 175 AB - We study the spaces
$H_{μ}(Ω) = {f: Ω → ℂ holomorphic: ∫_{0}^{R} ∫_{0}^{2π} |f(re^{iφ})| dφdμ(r) < ∞}$
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 $(∑ ⊕ Aₙ)_{(1)}$. Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere. LA - eng KW - Hardy space; isomorphism UR - http://eudml.org/doc/285697 ER -