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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
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Category: math
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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
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Date available: 2009-09-24T11:53:49Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128248
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Reference: [1] B. R.  Choe, H.  Koo, and H.  Yi: Positive Toeplitz operators between the harmonic Bergman spaces.Potential Anal. 17 (2002), 307–335. MR 1918239, 10.1023/A:1016356229211
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
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
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