Positive Toeplitz operators of Schatten-Herz type

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Abstract

Motivated by a recent work of Loaiza et al. for the holomorphic case on the disk, we introduce and study the notion of Schatten-Herz type Toeplitz operators acting on the harmonic Bergman space of the ball. We obtain characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions. Our characterization in terms of Berezin transforms settles a question posed by Loaiza et al.

Original languageEnglish
Pages (from-to)31-62
Number of pages32
JournalNagoya Mathematical Journal
Volume185
Publication statusPublished - 2007 Mar 30

ASJC Scopus subject areas

  • Mathematics(all)

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