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    Rozenblum, G. and Vasilevski, N. 2016. Toeplitz Operators Defined by Sesquilinear Forms: Bergman Space Case. Journal of Mathematical Sciences, Vol. 213, Issue. 4, p. 582.

  • Proceedings of the Edinburgh Mathematical Society, Volume 54, Issue 2
  • June 2011, pp. 505-514

Toeplitz operators with distributional symbols on Bergman spaces

  • Antti Perälä (a1), Jari Taskinen (a1) and Jani Virtanen (a2)
  • DOI:
  • Published online: 07 April 2011

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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2.A. Alexandrov and G. Rozenblum , Finite rank Toeplitz operators: some extensions of D. Luecking's theorem, J. Funct. Analysis 256 (2009), 22912303.

3.S. Axler and D. Zheng , Compact operators via the Berezin transform, Indiana Univ. Math. J. 47 (1998), 387400.

7.D. Suarez , The essential norm of operators in the Toeplitz algebra on $A^p(\mathbb{B}_n)$, Indiana Univ. Math. J. 56 (2007), 21852232.

12.K. Zhu , BMO and Hankel operators on Bergman spaces, Pac. J. Math. 155 (1992), 377395.

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
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