Toeplitz operators and herz spaces on the half-space

Boo Rim Choe, Kyesook Nam

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume59
Issue number4
DOIs
Publication statusPublished - 2007 Dec 1

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Herz Space
Operator Space
Toeplitz Operator
Half-space
Ball
Berezin Transform
Positive Operator
Compactness
Boundedness
Continue
Range of data
Class

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Toeplitz operators and herz spaces on the half-space. / Choe, Boo Rim; Nam, Kyesook.

In: Integral Equations and Operator Theory, Vol. 59, No. 4, 01.12.2007, p. 501-521.

Research output: Contribution to journalArticle

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