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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-3-3,
author = {Anahit Harutyunyan and Wolfgang Lusky},
title = {On the boundedness of the differentiation operator between weighted spaces of holomorphic functions},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {233-247},
zbl = {1142.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-3-3}
}
Anahit Harutyunyan; Wolfgang Lusky. On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Mathematica, Tome 187 (2008) pp. 233-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-3-3/