Composition operators on weighted Bergman spaces of a half-plane

By Sam Elliott, Andrew Wynn. Proceedings of the Edinburgh Mathematical Society, 2009

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Abstract We use induction and interpolation techniques to prove that a composition operator induced by a map ϕ is bounded on the weighted Bergman space $\mathcal{A}^2_\alpha(\mathbb{H})$ of the right half-plane if and only if ϕ fixes the point at ∞ non-tangentially and if it has a finite angular derivative λ there. We further prove that in this case the norm, the essential norm and the spectral radius of the operator are all equal and are given by λ(2+α)/2.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/17498436360c6f0a516ec8205e5f320f6d1d535d