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Compactness of composition operators acting on weighted Bergman-Orlicz spaces

100%

Sharma A., Ueki S.

Annales Polonici Mathematici

2012

tom 103

nr 1

1-13

We characterize compact composition operators acting on weighted Bergman-Orlicz spaces $𝓐^{ψ}_α = {f ∈ H(𝔻) : ∫_{𝔻} ψ(|f(z)|) dA_α(z) < ∞}$, 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 $𝓐^{ψ}_α$ if and only if it is compact on the weighted Bergman space $𝓐²_{α}$.

Composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk

100%

Stević S., Sharma A.

Annales Polonici Mathematici

2012

tom 105

nr 1

77-86

We characterize the boundedness and compactness of composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Sharma A.

1 Stević S.

1 Ueki S.

2 2012

Wyniki wyszukiwania

Compactness of composition operators acting on weighted Bergman-Orlicz spaces

Composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk