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Toeplitz operators with distributional symbols on Bergman spaces

  • Antti Perälä (a1), Jari Taskinen (a1) and Jani Virtanen (a2)

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

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13. K. Zhu , Operator theory in function spaces, 2nd edn, Mathematical Surveys and Monographs 138 (American Mathematical Society, Providence, RI, 2007).

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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