On the boundedness of the differentiation operator between weighted spaces of holomorphic functions

Anahit Harutyunyan, and Wolfgang Lusky. "On the boundedness of the differentiation operator between weighted spaces of holomorphic functions." Studia Mathematica 184.3 (2008): 233-247. <http://eudml.org/doc/285343>.

@article{AnahitHarutyunyan2008,
abstract = {We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.},
author = {Anahit Harutyunyan, Wolfgang Lusky},
journal = {Studia Mathematica},
keywords = {differentiation operator; holomorphic functions; weighted spaces},
language = {eng},
number = {3},
pages = {233-247},
title = {On the boundedness of the differentiation operator between weighted spaces of holomorphic functions},
url = {http://eudml.org/doc/285343},
volume = {184},
year = {2008},
}

TY - JOUR
AU - Anahit Harutyunyan
AU - Wolfgang Lusky
TI - On the boundedness of the differentiation operator between weighted spaces of holomorphic functions
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 3
SP - 233
EP - 247
AB - We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
LA - eng
KW - differentiation operator; holomorphic functions; weighted spaces
UR - http://eudml.org/doc/285343
ER -