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Positive Toeplitz Operators of Schatten–Herz Type

Published online by Cambridge University Press:  11 January 2016

Boorim Choe ,
Hyungwoon Koo  and
Kyunguk Na
Boorim Choe
Affiliation:
Department of Mathematics, Korea University, Seoul 136-713, Koreacbr@korea.ac.kr
Hyungwoon Koo
Affiliation:
Department of Mathematics Korea University, Seoul 136-713, KOREA, koohw@korea.ac.kr
Kyunguk Na
Affiliation:
Department of Mathematics Korea University, Seoul 136-713, Korea, nakyunguk@korea.ac.kr
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Abstract

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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.

Keywords

47B3546E30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 185 , 2007 , pp. 31 - 62
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

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