Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T08:38:33.845Z Has data issue: false hasContentIssue false
  • English
  • Français

A CHARACTERISATION OF BERGMAN SPACES ON THE UNIT BALL OF ℂn

Published online by Cambridge University Press:  01 May 2009

SONGXIAO LI ,
HASI WULAN ,
RUHAN ZHAO  and
KEHE ZHU
SONGXIAO LI
Affiliation:
Department of Mathematics, Jiaying University, Guangdong, China e-mail: lsx@mail.zjxu.edu.cn
HASI WULAN
Affiliation:
Department of Mathematics, shantou university, Guangdong, China e-mail: wulan@stu.edu.cn
RUHAN ZHAO
Affiliation:
Department of Mathematics, SUNY, Brockport, NY 14420, USA e-mail: rzhao@brockport.edu
KEHE ZHU
Affiliation:
Department of Mathematics, SUNY, Albany, NY 12222, USA e-mail: kzhu@math.albany.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain a new characterisation for weighted Bergman spaces Apα on the unit ball n of ℂn in terms of a double integral of the functions |f(z) − f(w)|/|z − w| and |f(z) − f(w)|/|1 − 〈 z, w〉|.

Keywords

32A36
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 315 - 330
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Holland, F. and Walsh, D., Criteria for membership of Bloch space and its subspace, BMOA, Math. Ann. 273 (1986), 317–335.CrossRefGoogle Scholar
2.Kwon, E., A characterization of Bloch space and Besov space, J. Math. Anal. Appl. 324 (2006), 1429–1437.CrossRefGoogle Scholar
3.Li, S. and Wulan, H., Besov spaces on the unit ball of ℂn, Indian J. Math. 48 (2006), 177–186.Google Scholar
4.Nowark, M., Bloch and Möbius invariant Besov spaces on the unit ball in ℂn, Complex Var. 44 (2001), 1–12.Google Scholar
5.Ren, G. and Tu, C., Bloch spaces in the unit ball of ℂn, Proc. Am. Math. Soc. 133 (2005), 719–726.CrossRefGoogle Scholar
6.Rudin, W., Function Theory in the Unit Ball of ℂn (Springer-Verlag, New York, 1980).CrossRefGoogle Scholar
7.Stein, E. and Weiss, G., Interpolation of operators with change of measures, Trans. Am. Math. Soc. 87 (1958), 159–172.CrossRefGoogle Scholar
8.Stessin, M. and Zhu, K., Composition operators on embedded disks, J. Operator Theory 56 (2006), 423–449.Google Scholar
9.Stroethoff, K., On Besov-type space characterizations for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), 405–420.CrossRefGoogle Scholar
10.Stroethoff, K., The Bloch space and Besov spaces of analytic functions, Bull. Austral. Math. Soc. 54 (1996), 211–219.CrossRefGoogle Scholar
11.Wulan, H. and Zhu, K., Lipschitz type characterizations for Bergman spaces, Can. Math. Bull. (in press).Google Scholar
12.Yoneda, R., Characterizations of Bloch space and Besov spaces by oscillations, Hokkaido Math. J. 29 (2000), 409–451.CrossRefGoogle Scholar
13.Zhao, R., A characterization of Bloch type spaces on the unit ball of ℂn, J. Math. Anal. Appl. 330 (2007), 291–297.CrossRefGoogle Scholar
14.Zhao, R. and Zhu, K., Theory of Bergman spaces in the unit ball, Mém. Soc. Math. Fr. (in press).Google Scholar
15.Zhu, K., Operator theory in function spaces, second edition (American Mathematical Society, Providence, RI, 2007).CrossRefGoogle Scholar
16.Zhu, K., Spaces of holomorphic functions in the unit ball (Springer-Verlag, New York, 2005).Google Scholar