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Schatten class positive Toeplitz operators on Bergman spaces of the Siegel upper half-space

Abstract

We characterize Schatten class membership of positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space in terms of averaging functions and Berezin transforms in the range of \(0<p<\infty \).

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Acknowledgements

The author is grateful to the referee for pointing out a few typos. He also wishes to express his gratitude to his tutor Professor Congwen Liu for warm encouragement.

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Correspondence to Jiajia Si.

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This work was supported by the National Natural Science Foundation of China Grant 11971453.

Communicated by Adrian Constantin.

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Si, J. Schatten class positive Toeplitz operators on Bergman spaces of the Siegel upper half-space. Monatsh Math 196, 335–355 (2021). https://doi.org/10.1007/s00605-021-01609-6

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Keywords

  • Toeplitz operators
  • Schatten classes
  • Bergman spaces
  • Siegel upper half-space
  • Berezin transform

Mathematics Subject Classification

  • Primary 47B35
  • Secondary 32A36