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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Commuting Toeplitz operators with pluriharmonic symbols


Author: Dechao Zheng
Journal: Trans. Amer. Math. Soc. 350 (1998), 1595-1618
MSC (1991): Primary 47B35
MathSciNet review: 1443898
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Abstract: By making use of $\mathcal M$-harmonic function theory, we characterize commuting Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball or on the Hardy space of the unit sphere in $n$-dimensional complex space.


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Additional Information

Dechao Zheng
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Address at time of publication: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: zheng@math.vanderbilt.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02051-0
PII: S 0002-9947(98)02051-0
Keywords: Toeplitz operator, Bergman space, Hardy space, pluriharmonic function, ${\mathcal M}$-harmonic function
Received by editor(s): June 30, 1995
Received by editor(s) in revised form: July 15, 1996
Additional Notes: Supported in part by the National Science Foundation.
Article copyright: © Copyright 1998 American Mathematical Society