Toeplitz operators and herz spaces on the half-space

Boo Rim Choe, Kyesook Nam

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


On the setting of the half-space we introduce the Schatten-Herz classes of Toeplitz operators and obtain characterizations for positive Toeplitz operators to belong to those classes. We also prove results concerning the boundedness and compactness of Toeplitz operators with Herz symbols. Such a study has been recently done on the ball. At a critical step of the proofs we employ a much simplified argument to extend the range of parameters for Herz spaces on which the Berezin transform is bounded. Our results show not only that most of results on the ball continue to hold, but also that there is some pathology caused by the unboundedness of the domain.

Original languageEnglish
Pages (from-to)501-521
Number of pages21
JournalIntegral Equations and Operator Theory
Issue number4
Publication statusPublished - 2007 Dec

Bibliographical note

Funding Information:
The first author was in part supported by a Korea University Grant(2007), the second author was in part supported by Hanshin University Research Grant, and both authors were in part supported by KOSEF(R01-2003-000-10243-0).


  • Half-space
  • Harmonic Bergman space
  • Schatten-Herz class
  • Toeplitz operator

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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