Positive Toeplitz operators between the harmonic Bergman spaces

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26 Citations (Scopus)

Abstract

On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space bp into another bq for 1 < p < ∞, 1 < q < ∞. The case p = 1 or q = 1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b2 to be in the Schatten classes. Some applications are also included.

Original languageEnglish
Pages (from-to)307-335
Number of pages29
JournalPotential Analysis
Volume17
Issue number4
DOIs
Publication statusPublished - 2002

Keywords

  • Carleson measures
  • Half-space
  • Harmonic Bergman functions
  • Multipliers
  • Positive Toeplitz operators

ASJC Scopus subject areas

  • Analysis

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