Articles

COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

  • Dai-Ji-Neng ,
  • OUYANG Cai-Heng
Expand
  • 1. School of Science, Wuhan Institute of Technology, Wuhan 430074, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
    3. Wuhan Institute of Physics and Mathematics, the Chinese Academy of Science, Wuhan 430071, China

Received date: 2012-11-19

  Online published: 2014-01-20

Supported by

Supported in part by the National Natural Science Foundation of China (11301404, 11271359) and the Educational Commission of Hubei Province of China (Q20121503).

Abstract

In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators CΦ between Bloch type spaces in the unit ball Bn.

Cite this article

Dai-Ji-Neng , OUYANG Cai-Heng . COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL[J]. Acta mathematica scientia, Series B, 2014 , 34(1) : 73 -81 . DOI: 10.1016/S0252-9602(13)60127-7

References

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

[2] Chen H, Gauthier P. Composition operators on μ-Bloch spaces. Canad J Math, 2009, 61(1): 50–75

[3] Cowen C, MacCluer B. Composition Operators on Spaces of Analytic Functions. Boca Raton: CRC Press, 1995

[4] Madigan K, Matheson A. Compact composition operators on the Bloch space. Trans Amer Math Soc, 1995, 347(7): 2679–2687

[5] Montes-Rodr´?guez A. The essential norms of a composition operator on Bloch spaces. Pacific J Math, 1999, 188: 339–351

[6] Xiao J. Composition operators associated with Bloch-type spaces. Complex Variables, 2001, 46: 109–121

[7] Wulan H, Zheng D, Zhu K. Compact composition operators on BMOA and the Bloch space. Proc Amer Math Soc, 2009, 137: 3861–3868

[8] Zhao R. Essential norms of composition operators between Bloch type spaces. Proc Amer Math Soc, 2010, 138: 2537–2546

[9] Shi J, Luo L. Composition operators on the Bloch space of several complex variables. Acta Math Sin, 2000, 16(1): 85–98

[10] Dai J. Compact composition operators on the Bloch space of the unit ball. J Math Anal Appl, 2012, 386: 294–299

[11] Liu J, Li J, Zhang X. Characterizations of composition operators between Bloch type spaces on the unit ball. Acta Mathematica Sinica, Chinese Series, 2007, 50: 711–720

[12] Tjani M. Compact composition operators on Besov spaces. Trans Amer Math Soc, 2003, 355(11): 4683–4698

Outlines

/