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Trace Class Toeplitz Operators with Singular Symbols

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Abstract

We provide sufficient conditions for Toeplitz operators with distributional symbols acting on the Bergman space on the unit disk to be trace class. The Berezin transform of distributions, introduced in the paper, yields a formula for the trace. Several instructive examples are also given.

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Acknowledgments

The first author is grateful to CINVESTAV for hospitality.

Funding

The work of the first author is supported by the Russian Science Foundation under grant 20-11-20032.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96, Gothenburg, Sweden

    Grigori V. Rozenblum

  2. Faculty of Physics, St. Petersburg State University, Petergof, Ul’yanovskaya ul. 1, St. Petersburg, 198504, Russia

    Grigori V. Rozenblum

  3. Departamento de Matemáticas, Cinvestav, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, CP 07360, Mexico

    Nikolai L. Vasilevski

Authors
  1. Grigori V. Rozenblum
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  2. Nikolai L. Vasilevski
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Correspondence to Grigori V. Rozenblum.

Additional information

To Armen Sergeev on the occasion of his 70th birthday

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Rozenblum, G.V., Vasilevski, N.L. Trace Class Toeplitz Operators with Singular Symbols. Proc. Steklov Inst. Math. 311, 225–232 (2020). https://doi.org/10.1134/S0081543820060140

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  • DOI: https://doi.org/10.1134/S0081543820060140

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