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Commuting Toeplitz operators with harmonic symbols

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Abstract

This paper shows that on the Bergman space, two Toeplitz operators with harmonic symbols commute only in the obvious cases. The main tool is a characterization of harmonic functions by a conformally invariant mean value property.

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References

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA

    Sheldon Axler & Željko Čučković

  2. Faculty of Technology, University of Zagreb, Pierottijeva 6, Zagreb, Yugoslavia

    Željko Čučković

Authors
  1. Sheldon Axler
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  2. Željko Čučković
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Additional information

The first author was partially supported by the National Science Foundation.

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Axler, S., Čučković, Ž. Commuting Toeplitz operators with harmonic symbols. Integr equ oper theory 14, 1–12 (1991). https://doi.org/10.1007/BF01194925

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  • DOI: https://doi.org/10.1007/BF01194925

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