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

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 -