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Composition operators on Qp spaces

Part of: Special classes of linear operators Linear function spaces and their duals

Published online by Cambridge University Press:  09 April 2009

Zengjian Lou
Zengjian Lou
Affiliation:
Centre for Mathematics and its Applications School of Mathematical Sciences The Australian National UniversityCanberra ACT 0200Australia e-mail: lou@maths.anu.edu.au
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Abstract

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A holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.

Keywords

composition operatorsQp spacesDirichlet spaceBMOABloch space

MSC classification

Secondary: 47B38: Operators on function spaces (general) 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 2 , April 2001 , pp. 161 - 188
Copyright
Copyright © Australian Mathematical Society 2001

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