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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation pp 133–157Cite as

Birkhäuser

Weighted Composition Operators from the Analytic Besov Spaces to BMOA

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

Let ψ and \( \varphi \) be analytic functions on the open unit disk \( (\mathbb{D}) \) with \( \varphi(\mathbb{D})\sqsubseteq\mathbb{D}\, {\rm and\, let }\, 1\leq p<\infty \). We characterize the bounded and the compact weighted composition operators \( {W_{\psi\varphi}} \) from the analytic Besov space B p into BMOA and into VMOA. We also show that there are no isometries among the composition operators.

Mathematics Subject Classification (2010). Primary: 47B38, 30H35, 30H30; Secondary: 30H10.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA

    Flavia Colonna

  2. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA

    Maria Tjani

Authors
  1. Flavia Colonna
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  2. Maria Tjani
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Corresponding author

Correspondence to Flavia Colonna .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Colonna, F., Tjani, M. (2014). Weighted Composition Operators from the Analytic Besov Spaces to BMOA. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_8

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