| Title:
|
Positive Toeplitz operators between the pluriharmonic Bergman spaces (English) |
| Author:
|
Choi, Eun Sun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
93-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space $b^p$ into another $b^q$ for $1 < p, q < \infty $ in terms of certain Carleson and vanishing Carleson measures. (English) |
| Keyword:
|
Toeplitz operators |
| Keyword:
|
pluriharmonic Bergman spaces |
| Keyword:
|
Carleson measure |
| MSC:
|
31B05 |
| MSC:
|
31C10 |
| MSC:
|
46E15 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 1174.47021 |
| idMR:
|
MR2402528 |
| . |
| Date available:
|
2009-09-24T11:53:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128248 |
| . |
| Reference:
|
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| Reference:
|
[2] B. R. Choe, Y. J. Lee, and K. Na: Positive Toeplitz operators from a harmonic Bergman space into another.Tohoku Math. J. 56 (2004), 255–270. MR 2053321, 10.2748/tmj/1113246553 |
| Reference:
|
[3] E. S. Choi: Positive Toeplitz operators on pluriharmonic Bergman spaces.J. Math. Kyoto Univ. 47 (2007), 247–267. Zbl 1158.32001, MR 2376957, 10.1215/kjm/1250281046 |
| Reference:
|
[4] D. Luecking: Embedding theorem for spaces of analytic functions via Khinchine’s inequality.Mich. Math. J. 40 (1993), 333–358. MR 1226835, 10.1307/mmj/1029004756 |
| Reference:
|
[5] J. Miao: Toeplitz operators on harmonic Bergman spaces.Integral Equations Oper. Theory 27 (1997), 426–438. Zbl 0902.47026, MR 1442127, 10.1007/BF01192123 |
| Reference:
|
[6] K. Zhu: Operator Theory in Function Spaces.Marcell Dekker, New York, 1990. Zbl 0706.47019, MR 1074007 |
| Reference:
|
[7] K. Zhu: Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains.J. Oper. Theory 20 (1988), 329–357. Zbl 0676.47016, MR 1004127 |
| Reference:
|
[8] W. Rudin: Function Theory in the Unit Ball of $\mathbb{C}^n$.Springer-Verlag, New York, 1980. MR 0601594 |
| . |
