On L₁-subspaces of holomorphic functions

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 -