Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure
Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure
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.
References:
[1] B. R. Choe, H. Koo, and H. Yi: Positive Toeplitz operators between the harmonic Bergman spaces. Potential Anal. 17 (2002), 307–335. DOI 10.1023/A:1016356229211 | MR 1918239
[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. DOI 10.2748/tmj/1113246553 | MR 2053321
[3] E. S. Choi: Positive Toeplitz operators on pluriharmonic Bergman spaces. J. Math. Kyoto Univ. 47 (2007), 247–267. DOI 10.1215/kjm/1250281046 | MR 2376957 | Zbl 1158.32001
[4] D. Luecking: Embedding theorem for spaces of analytic functions via Khinchine’s inequality. Mich. Math. J. 40 (1993), 333–358. DOI 10.1307/mmj/1029004756 | MR 1226835
[5] J. Miao: Toeplitz operators on harmonic Bergman spaces. Integral Equations Oper. Theory 27 (1997), 426–438. DOI 10.1007/BF01192123 | MR 1442127 | Zbl 0902.47026
[6] K. Zhu: Operator Theory in Function Spaces. Marcell Dekker, New York, 1990. MR 1074007 | Zbl 0706.47019
[7] K. Zhu: Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains. J. Oper. Theory 20 (1988), 329–357. MR 1004127 | Zbl 0676.47016
[8] W. Rudin: Function Theory in the Unit Ball of $\mathbb{C}^n$. Springer-Verlag, New York, 1980. MR 0601594
Search
Partner of
