On the isomorphism classes of weighted spaces of harmonic and holomorphic functions

Wolfgang Lusky

Studia Mathematica (2006)

  • Volume: 175, Issue: 1, page 19-45
  • ISSN: 0039-3223

Abstract

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Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of H v = f : Ω → ℂ h o l o m o r p h i c : s u p z ∈ Ω | f ( z ) | v ( z ) < ∞ and investigate some isomorphism classes of h v = f : Ω → ℂ h a r m o n i c : s u p 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 H v ∼ l ∞ or H v ∼ H ∞ , and at least two possibilities for hv, again h v ∼ l ∞ and h v ∼ H ∞ . We also discuss many new examples of weights.

How to cite

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Wolfgang Lusky. "On the isomorphism classes of weighted spaces of harmonic and holomorphic functions." Studia Mathematica 175.1 (2006): 19-45. <http://eudml.org/doc/285212>.

@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 -

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