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Toeplitz operators with distributional symbols on Bergman spaces
Published online by Cambridge University Press: 07 April 2011
Abstract
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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- Research Article
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- Copyright © Edinburgh Mathematical Society 2011
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