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Toeplitz operators with distributional symbols on Bergman spaces


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Perälä, A., Taskinen, J. and Virtanen, J. (2011) Toeplitz operators with distributional symbols on Bergman spaces. Proceedings of the Edinburgh Mathematical Society, 54 (02). pp. 505-514. ISSN 1464-3839

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To link to this article DOI: 10.1017/S001309151000026X


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.

Item Type:Article
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:29124
Publisher:Edinburgh Mathematical Society

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