@article{WolfgangLusky2006,
abstract = {Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of
$Hv = \{f: Ω → ℂ holomorphic: sup_\{z∈ Ω\} |f(z)|v(z) < ∞\}$
and investigate some isomorphism classes of
$hv = \{f: Ω → ℂ harmonic : sup_\{z∈ Ω\} |f(z)|v(z) < ∞\}$
where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either $Hv ∼ l_\{∞\}$ or $Hv ∼ H_\{∞\}$, and at least two possibilities for hv, again $hv ∼ l_\{∞\}$ and $hv ∼ H_\{∞\}$. We also discuss many new examples of weights.},
author = {Wolfgang Lusky},
journal = {Studia Mathematica},
keywords = {holomorphic functions; harmonic functions; weighted spaces},
language = {eng},
number = {1},
pages = {19-45},
title = {On the isomorphism classes of weighted spaces of harmonic and holomorphic functions},
url = {http://eudml.org/doc/285212},
volume = {175},
year = {2006},
}
TY - JOUR
AU - Wolfgang Lusky
TI - On the isomorphism classes of weighted spaces of harmonic and holomorphic functions
JO - Studia Mathematica
PY - 2006
VL - 175
IS - 1
SP - 19
EP - 45
AB - Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of
$Hv = {f: Ω → ℂ holomorphic: sup_{z∈ Ω} |f(z)|v(z) < ∞}$
and investigate some isomorphism classes of
$hv = {f: Ω → ℂ harmonic : sup_{z∈ Ω} |f(z)|v(z) < ∞}$
where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either $Hv ∼ l_{∞}$ or $Hv ∼ H_{∞}$, and at least two possibilities for hv, again $hv ∼ l_{∞}$ and $hv ∼ H_{∞}$. We also discuss many new examples of weights.
LA - eng
KW - holomorphic functions; harmonic functions; weighted spaces
UR - http://eudml.org/doc/285212
ER -
