Author:
Elliott Sam J.,Wynn Andrew
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Reference9 articles.
1. 5. Elliott S. J. and Jury M. T. , Composition operators on Hardy spaces of a half plane, Bull. Lond. Math. Soc., in press.
2. Composition operators on Hardy spaces of a half-plane
3. Interpolation Spaces
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