ON COMPACTNESS FOR ITERATED COMMUTATORS

doi:10.1016/S0252-9602(11)60250-6

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 491-500.doi: 10.1016/S0252-9602(11)60250-6

ON COMPACTNESS FOR ITERATED COMMUTATORS

刘永民|于燕燕

Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China； School of Mathematics and Physics |Science, Xuzhou Institute of Technology, Xuzhou 221008, China

收稿日期:2008-09-23 修回日期:2009-04-02 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
Supported by the National Natural Science Foundation of China (10471039) and the Grant of Higher Schools' Natural Science Basic Research of Jiangsu Province of China (06KJD110175; 07KJB110115)

ON COMPACTNESS FOR ITERATED COMMUTATORS

LIU Yong-Min, YU Yan-Yan

Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China； School of Mathematics and Physics |Science, Xuzhou Institute of Technology, Xuzhou 221008, China

Received:2008-09-23 Revised:2009-04-02 Online:2011-03-20 Published:2011-03-20
Supported by:
Supported by the National Natural Science Foundation of China (10471039) and the Grant of Higher Schools' Natural Science Basic Research of Jiangsu Province of China (06KJD110175; 07KJB110115)

摘要/Abstract

摘要：

The authors study the iterated commutators on the weighted Bergman spaces A²(Φ), and prove that C^n/h is compact on A²(Φ) if and only if h ∈B₀.

关键词: Weighted Bergman space, iterated commutator, normal function, little Bloch function, compactness

Abstract:

The authors study the iterated commutators on the weighted Bergman spaces A²(Φ), and prove that C^n/h is compact on A²(Φ) if and only if h ∈B₀.

Key words: Weighted Bergman space, iterated commutator, normal function, little Bloch function, compactness

中图分类号:

47B38

刘永民, 于燕燕. ON COMPACTNESS FOR ITERATED COMMUTATORS[J]. 数学物理学报(英文版), 2011, 31(2): 491-500.

LIU Yong-Min, YU Yan-Yan. ON COMPACTNESS FOR ITERATED COMMUTATORS[J]. Acta mathematica scientia,Series B, 2011, 31(2): 491-500.

[1] Fan D, Wu Z. Norm estimates for iterated commutators on the Bergman spaces of the unit ball. Amer J Math, 1995, 117(2): 523--543

[2] Axler S. The Bergman space, the Bloch space, and commutators of multiplication operators. Duke Math J, 1986, 53(2): 315--332

[3] Xiao J. Boundedness and compactness for Hankel operators on A²(Φ). Adv in Math (China), 1993, 22(2): 146--159

[4] Békollé D, Berger C A, Coburn L A, et al. BMO in the Bergman metric on bounded symmetric domains. J Funct Anal, 1990, 93(2): 310--350

[5] Arazy J, Fisher S D, Janson S, et al. Membership of Hankel operators on the ball in unitary ideals. J London Math Soc (2), 1991, 43(3): 485--508

[6] Zhu K. BMO and Hankel operators on Bergman spaces. Pacific J Math, 1992, 155(2): 377--395

[7] Xiao J. Compactness for Toeplitz and Hankel operators on weighted Bergman spaces of ball in Cⁿ. Sci China, Ser A, 1993, 36(10): 1153--1161

[8] Xiao J. Compactness of both Toeplitz and Hankel operators on the Bergman space A². Chinese Ann Math (in Chinese), Ser A, 1994, 15(2): 145--154

[9] Liu Y, Hu Z. Boundedness for iterated commutators on the mixed norm spaces. J Math Anal Appl, 2007, 332(2): 787--797

[10] Zhang X, Xiao J, Hu Z. The multipliers between the mixed norm spaces in C^m. J Math Anal Appl, 2005, 311(2): 664--674

[11] Tan H. Weighted Bergman spaces and Carleson measures on the unit ball of Cⁿ. Anal Math, 2000, 26(2): 119--132

[12] Ren G, Shi J. Bergman type operator on mixed norm spaces with applications. Chinese Ann Math, Ser B, 1997, 18(3): 265--276

[13] Timoney R M. Bloch functions in several complex variables I. Bull London Math Soc, 1980, 12(4): 241--267

[14] Zhu K. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer, 2005

[15] Rudin W. Function Theory in the Unit Ball of Cⁿ. New York-Berlin: Springer-Verlag, 1980

[16] Jevti$\acute{\hbox{c}}$ M. Bounded projections and duality in mixed-norm spaces of analytic functions. Complex Variables Theory Appl, 1987, 8(3/4): 293--301

[17] Gu D. Bergman projections and duality in weighted mixed-norm spaces of analytic functions. Michigan Math J, 1992, 39(1): 71--84

[18] Shi J. Duality and multipliers for mixed norm spaces in the ball I, II. Complex Variables Theory Appl, 1994, 25(2): 119--130; 131--157

[19] Shields A L, Williams D L. Bounded projections, duality, and multipliers in spaces of analytic functions. Trans Amer Math Soc, 1971, 162: 287--302

[20] Timoney R M. Bloch functions in several complex variables II. J Reine Angew Math, 1980, 319: 1--22

ON COMPACTNESS FOR ITERATED COMMUTATORS

ON COMPACTNESS FOR ITERATED COMMUTATORS

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