Compactness of composition operators acting on weighted Bergman-Orlicz spaces

Ajay K. Sharma, and S. Ueki. "Compactness of composition operators acting on weighted Bergman-Orlicz spaces." Annales Polonici Mathematici 103.1 (2012): 1-13. <http://eudml.org/doc/280283>.

@article{AjayK2012,
abstract = {We characterize compact composition operators acting on weighted Bergman-Orlicz spaces $^\{ψ\}_α = \{f ∈ H() : ∫_\{\} ψ(|f(z)|) dA_α(z) < ∞\}$, where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition $lim_\{t → ∞\} ψ(t)/t = ∞$ and the Δ₂-condition. In fact, we prove that $C_\{φ\}$ is compact on $^\{ψ\}_α$ if and only if it is compact on the weighted Bergman space $²_\{α\}$.},
author = {Ajay K. Sharma, S. Ueki},
journal = {Annales Polonici Mathematici},
keywords = {weighted Bergman-Orlicz space; composition operator; vanishing Carleson measure; Nevanlinna counting function},
language = {eng},
number = {1},
pages = {1-13},
title = {Compactness of composition operators acting on weighted Bergman-Orlicz spaces},
url = {http://eudml.org/doc/280283},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Ajay K. Sharma
AU - S. Ueki
TI - Compactness of composition operators acting on weighted Bergman-Orlicz spaces
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 1
SP - 1
EP - 13
AB - We characterize compact composition operators acting on weighted Bergman-Orlicz spaces $^{ψ}_α = {f ∈ H() : ∫_{} ψ(|f(z)|) dA_α(z) < ∞}$, where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition $lim_{t → ∞} ψ(t)/t = ∞$ and the Δ₂-condition. In fact, we prove that $C_{φ}$ is compact on $^{ψ}_α$ if and only if it is compact on the weighted Bergman space $²_{α}$.
LA - eng
KW - weighted Bergman-Orlicz space; composition operator; vanishing Carleson measure; Nevanlinna counting function
UR - http://eudml.org/doc/280283
ER -