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Compactness of composition operators acting on weighted Bergman-Orlicz spaces

Ajay K. SharmaS. Ueki — 2012

Annales Polonici Mathematici

We characterize compact composition operators acting on weighted Bergman-Orlicz spaces α ψ = f H ( ) : ψ ( | f ( z ) | ) d A 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 l i m t ψ ( t ) / t = 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 .

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