Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

Mohammad Ali Ardalani; Wolfgang Lusky

Studia Mathematica (2012)

  • Volume: 209, Issue: 3, page 225-234
  • ISSN: 0039-3223

Abstract

top
Let v be a standard weight on the upper half-plane , i.e. v: → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ , v(it) ≥ v(is) if t ≥ s > 0 and l i m t 0 v ( i t ) = 0 . Put v₁(w) = Im wv(w), w ∈ . We characterize boundedness and surjectivity of the differentiation operator D: Hv() → Hv₁(). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv().

How to cite

top

Mohammad Ali Ardalani, and Wolfgang Lusky. "Bounded operators on weighted spaces of holomorphic functions on the upper half-plane." Studia Mathematica 209.3 (2012): 225-234. <http://eudml.org/doc/285780>.

@article{MohammadAliArdalani2012,
abstract = {Let v be a standard weight on the upper half-plane , i.e. v: → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ , v(it) ≥ v(is) if t ≥ s > 0 and $lim_\{t→ 0\} v(it) = 0$. Put v₁(w) = Im wv(w), w ∈ . We characterize boundedness and surjectivity of the differentiation operator D: Hv() → Hv₁(). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv().},
author = {Mohammad Ali Ardalani, Wolfgang Lusky},
journal = {Studia Mathematica},
keywords = {differentiation operator; composition operator; holomorphic functions; weighted spaces; upper half-plane},
language = {eng},
number = {3},
pages = {225-234},
title = {Bounded operators on weighted spaces of holomorphic functions on the upper half-plane},
url = {http://eudml.org/doc/285780},
volume = {209},
year = {2012},
}

TY - JOUR
AU - Mohammad Ali Ardalani
AU - Wolfgang Lusky
TI - Bounded operators on weighted spaces of holomorphic functions on the upper half-plane
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 3
SP - 225
EP - 234
AB - Let v be a standard weight on the upper half-plane , i.e. v: → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ , v(it) ≥ v(is) if t ≥ s > 0 and $lim_{t→ 0} v(it) = 0$. Put v₁(w) = Im wv(w), w ∈ . We characterize boundedness and surjectivity of the differentiation operator D: Hv() → Hv₁(). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv().
LA - eng
KW - differentiation operator; composition operator; holomorphic functions; weighted spaces; upper half-plane
UR - http://eudml.org/doc/285780
ER -

NotesEmbed ?

top

You must be logged in to post comments.