| Title:
|
Commuting Toeplitz operators on the pluriharmonic Bergman space (English) |
| Author:
|
Lee, Young Joo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
535-544 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that two Toeplitz operators acting on the pluriharmonic Bergman space with radial symbol and pluriharmonic symbol respectively commute only in an obvious case. (English) |
| Keyword:
|
Toeplitz operators |
| Keyword:
|
pluriharmonic Bergman space |
| MSC:
|
31C10 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 1080.47028 |
| idMR:
|
MR2059271 |
| . |
| Date available:
|
2009-09-24T11:15:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127908 |
| . |
| Reference:
|
[1] A. Brown and P. R. Halmos: Algebraic properties of Toeplitz operators.J. Reine Angew. Math. 213 (1963/64), 89–102. MR 0160136 |
| Reference:
|
[2] B. R. Choe and Y. J. Lee: Commuting Toeplitz operators on the harmonic Bergman space.Michigan Math. J. 46 (1999), 163–174. MR 1682896, 10.1307/mmj/1030132367 |
| Reference:
|
[3] B. R. Choe and Y. J. Lee: Pluriharmonic symbols of commuting Toeplitz operators.Illinois J. Math. 37 (1993), 424–436. MR 1219648, 10.1215/ijm/1255987059 |
| Reference:
|
[4] . uković and N. V. Rao: Mellin transform, monomial symbols, and commuting Toeplitz operators.J. Funct. Anal. 154 (1998), 195–214. MR 1616532, 10.1006/jfan.1997.3204 |
| Reference:
|
[5] Y. J. Lee: Pluriharmonic symbols of commuting Toeplitz type operators.Bull. Austral. Math. Soc. 54 (1996), 67–77. Zbl 0881.47015, MR 1402993, 10.1017/S0004972700015082 |
| Reference:
|
[6] Y. J. Lee: Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces.Canad. Math. Bull. 41 (1998), 129–136. Zbl 0920.47024, MR 1624149, 10.4153/CMB-1998-020-7 |
| Reference:
|
[7] Y. J. Lee and K. Zhu: Some differential and integral equations with applications to Toeplitz operators.Integral Equation Operator Theory 44 (2002), 466–479. MR 1942036, 10.1007/BF01193672 |
| Reference:
|
[8] S. Ohno: Toeplitz and Hankel operators on harmonic Bergman spaces.Preprint. |
| Reference:
|
[9] W. Rudin: Function Theory in the Unit Ball of $\mathbb{C}^n$.Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 0601594 |
| Reference:
|
[10] D. Zheng: Commuting Toeplitz operators with pluriharmonic symbols.Trans. Amer. Math. Soc. 350 (1998), 1595–1618. Zbl 0893.47015, MR 1443898, 10.1090/S0002-9947-98-02051-0 |
| . |
