Compactness of composition operators acting on weighted Bergman–Orlicz spaces
Volume 103 / 2012
Annales Polonici Mathematici 103 (2012), 1-13
MSC: Primary 47B33, 46E10; Secondary 30D55.
DOI: 10.4064/ap103-1-1
Abstract
We characterize compact composition operators acting on weighted Bergman–Orlicz spaces where \alpha > -1 and \psi is a strictly increasing, subadditive convex function defined on [0 , \infty) and satisfying \psi(0) = 0, the growth condition \lim_{t \rightarrow \infty}\displaystyle \psi(t)/t = \infty and the \Delta_2-condition. In fact, we prove that C_{\varphi} is compact on \mathcal{A}^{\psi}_\alpha if and only if it is compact on the weighted Bergman space \mathcal{A}^{2}_{\alpha}.
