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Boundedness, Compactness and Schatten-class Membership of Weighted Composition Operators

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Abstract

The boundedness and compactness of weighted composition operators on the Hardy space \({{\mathcal H}^2}\) of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces \({\mathcal{A}^2_\alpha(\mathbb{D})}\) are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Zaragoza e IUMA, Plaza San Francisco s/n, 50009, Zaragoza, Spain

    E. A. Gallardo-Gutiérrez

  2. Department of Mathematics, University of Jammu, Jammu, 180 001, India

    R. Kumar

  3. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    J. R. Partington

Authors
  1. E. A. Gallardo-Gutiérrez
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  2. R. Kumar
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  3. J. R. Partington
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Correspondence to J. R. Partington.

Additional information

E. A. Gallardo-Gutiérrez and J. R. Partington are partially supported by Plan Nacional I + D grant no. MTM2007-61446 and Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref. DGA E-64. R. Kumar is partially supported by the Royal Society (UK) and the Department of Science and Technology (India).

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Gallardo-Gutiérrez, E.A., Kumar, R. & Partington, J.R. Boundedness, Compactness and Schatten-class Membership of Weighted Composition Operators. Integr. Equ. Oper. Theory 67, 467–479 (2010). https://doi.org/10.1007/s00020-010-1795-6

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  • DOI: https://doi.org/10.1007/s00020-010-1795-6

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