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 . 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().
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-3-2,
author = {Mohammad Ali Ardalani and Wolfgang Lusky},
title = {Bounded operators on weighted spaces of holomorphic functions on the upper half-plane},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {225-234},
zbl = {1262.46020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-3-2}
}
Mohammad Ali Ardalani; Wolfgang Lusky. Bounded operators on weighted spaces of holomorphic functions on the upper half-plane. Studia Mathematica, Tome 209 (2012) pp. 225-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-3-2/