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Toeplitz operators on the polydisk
Author(s):
Sunhua
Sun;
Dechao
Zheng
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3351-3356.
MSC (1991):
Primary 47B35
MathSciNet review:
1328380
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Abstract:
In this paper it is shown that two analytic Toeplitz operators essentially doubly commute if and only if they doubly commute on the Bergman space of the polydisk.
References:
- [AFR]
- P. Ahern, M. Flores and W. Rudin, An invariant volume-mean-value property, J. Funct. Anal. 111 (1993), 380--397. MR 94b:31002
- [AG]
- S. Axler and P. Gorkin, Algebras on the disk and doubly commuting operators, Trans. Amer. Math. Soc. 309 (1988), 711--723. MR 90a:46133
- [R]
- W. Rudin, Function theory on the polydiscs, Benjamin, New York, 1969. MR 41:501
- [SW]
- E. M. Stein and G. Weiss, Introduction to Fourier analysis on euclidean spaces, Princeton Univ. Press, 1971. MR 46:4102
- [Z]
- D. Zheng, Hankel operators and Toeplitz operators on the Bergman space, J. Funct. Anal. 83 (1989), 98--120. MR 91b:47057
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Additional Information:
Sunhua
Sun
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, People's Republic of China
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 3724
DOI:
10.1090/S0002-9939-96-03425-9
PII:
S 0002-9939(96)03425-9
Keywords:
Toeplitz operator,
Bergman space,
polydisk
Received by editor(s):
October 6, 1994
Received by editor(s) in revised form:
April 21, 1995
Additional Notes:
The first author was supported in part by the National Natural Science Foundation of China
The second author was supported in part by the National Science Foundation
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
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