Abstract
We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 1727-1749 |
| Number of pages | 23 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 356 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2004 May 1 |
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Keywords
- Bergman space
- N-harmonic function
- Toeplitz operator
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Commuting Toeplitz operators on the polydisk. / Choe, Boo Rim; Koo, Hyung Woon; Lee, Young Joo.
In: Transactions of the American Mathematical Society, Vol. 356, No. 5, 01.05.2004, p. 1727-1749.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Commuting Toeplitz operators on the polydisk
AU - Choe, Boo Rim
AU - Koo, Hyung Woon
AU - Lee, Young Joo
PY - 2004/5/1
Y1 - 2004/5/1
N2 - We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.
AB - We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.
KW - Bergman space
KW - N-harmonic function
KW - Toeplitz operator
UR - http://www.scopus.com/inward/record.url?scp=2142779149&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2142779149&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-03-03430-5
DO - 10.1090/S0002-9947-03-03430-5
M3 - Article
AN - SCOPUS:2142779149
VL - 356
SP - 1727
EP - 1749
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 5
ER -