a2 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (email@example.com)
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.
(Received February 01 2010)
(Online publication April 07 2011)
2010 Mathematics subject classification