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Weighted Composition Operators on BMOA

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Abstract

Let ψ and φ be analytic functions on the unit disk D such that φ(D) ⊂ D. We characterize the boundedness and compactness of the weighted composition operators f ↦ ψ · (f oφ) on BMOA, the space of analytic functions on D that have bounded mean oscillation on ∂D, and its subspace VMOA. We also provide estimates for the norm of a weighted composition operator on BMOA and its essential norm on VMOA. Finally, we use the above results to show that boundedness or compactness of a weighted composition operator on BMOA implies its boundedness or compactness on the Bloch space B, respectively.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68 (Gustaf Hällströmin katu 2b), FIN-00014 University of Helsinki, Finland

    Jussi Laitila

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  1. Jussi Laitila
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Correspondence to Jussi Laitila.

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The author was supported by the Finnish Academy of Science and Letters (Vilho, Yrjö and Kalle Väisälä Foundation) and the Academy of Finland, projects 53893, 210970 and 118422.

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Laitila, J. Weighted Composition Operators on BMOA. Comput. Methods Funct. Theory 9, 27–46 (2009). https://doi.org/10.1007/BF03321712

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  • DOI: https://doi.org/10.1007/BF03321712

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