Compactness of composition operators acting on weighted Bergman-Orlicz spaces

Ajay K. Sharma; S. Ueki

Ajay K. Sharma ; S. Ueki

Annales Polonici Mathematici, Tome 105 (2012), p. 1-13 / Harvested from The Polish Digital Mathematics Library

Résumé

We characterize compact composition operators acting on weighted Bergman-Orlicz spaces $_{α}^{ψ} = f \in H () : \int_{} ψ (| f (z) |) d A_{α} (z) < \infty$ , where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition $l i m_{t \to \infty} ψ (t) / t = \infty$ and the Δ₂-condition. In fact, we prove that $C_{φ}$ is compact on $_{α}^{ψ}$ if and only if it is compact on the weighted Bergman space $²_{α}$ .

Publié le : 2012-01-01

Zbl 1258.47041

EUDML-ID : urn:eudml:doc:280283

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     author = {Ajay K. Sharma and S. Ueki},
     title = {Compactness of composition operators acting on weighted Bergman-Orlicz spaces},
     journal = {Annales Polonici Mathematici},
     volume = {105},
     year = {2012},
     pages = {1-13},
     zbl = {1258.47041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-1-1}
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Ajay K. Sharma; S. Ueki. Compactness of composition operators acting on weighted Bergman-Orlicz spaces. Annales Polonici Mathematici, Tome 105 (2012) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-1-1/