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Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

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  • Roberto C. Raimondo

Abstract

We study the problem of the boundedness and compactness of 𠑇 𠜙 when 𠜙 ∈ ð ¿ 2 ( Ω ) and Ω is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of 𠑇 𠜙 .

Suggested Citation

  • Roberto C. Raimondo, 2011. "Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-26, August.
    • Handle: RePEc:hin:jijmms:164843
    DOI: 10.1155/2011/164843
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    Cited by:

    1. Roberto C. Raimondo, 2012. "Toeplitz Operators with Essentially Radial Symbols," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-14, January.

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