Toeplitz operators with distributional symbols on Bergman spaces
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
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.