Proceedings of the American Mathematical Society

Author(s): Guangbin Ren; Caifeng Tu
Journal: Proc. Amer. Math. Soc. 133 (2005), 719-726.
MSC (2000): Primary 32A18; Secondary 32A37
Posted: October 21, 2004
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Abstract: In this paper we obtain higher-dimensional versions of the Holland-Walsh characterization of the Bloch space and the Stroethoff characterization of the little Bloch space.

1.: L. V. Ahlfors, Möbius Transformations in Several Dimensions, Ordway Professorship Lectures in Mathematics, 1981. MR 84m:30028
2.: F. Beatrous and J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 256 (1989), 1-57. MR 90k:32010
3.: A. Bonami, J. Bruna and S. Grellier, On Hardy, BMO and Lipschitz spaces of invariantly harmonic functions in the unit ball, Proc. London Math. Soc. 77 (1998), 665-696. MR 99g:31008
4.: J. Burbea and S. Y. Li, Weighted Hadamard products of holomorphic functions in the ball, Pacific J. Math. 168 (1995), 235-270. MR 96d:32006
5.: J. S. Choe, H. O. Kim and Y. Y. Park, A Bergman-Carleson measure characterization of Bloch functions in the unit ball of $\mathbb{C}^{n}$ , Bull. Korean Math. Soc. 29 (1992), 285-293. MR 94e:32014
6.: F. Holland and D. Walsh, Criteria for membership of Bloch space and its subspace, BMOA, Math. Ann. 273 (1986), 317-335. MR 87k:30065
7.: K. T. Hahn and E. H. Youssfi, Möbius invariant Besov -spaces and Hankel operators in the Bergman space on the ball in $\mathbb{C}^{n}$ , Complex Variables 17 (1991), 89-104. MR 92m:47051
8.: M. Jevtic and M. Pavlovic, On $\mathcal{M}$ -harmonic Bloch space, Proc. Amer. Math. Soc. 123 (1995), 1385-1392. MR 95i:32009
9.: M. Nowak, Bloch space and Möbius invariant Besov spaces on the unit ball on $\mathbb{C}^{n}$ , Complex Variables 44 (2001), 1-12. MR 2002a:32003
10.: C. H. Ouyang, W. S. Yang and R. H. Zhao, Characterizations of Bergman spaces and Bloch space in the unit ball of $\mathbb{C}^{n}$ , Tran. Amer. Math. Soc. 374 (1995), 4301-4312. MR 96b:32006
11.: M. Pavlovic, Decompositions of $L\sp{p}$ and Hardy spaces of polyharmonic functions, J. Math. Anal. Appl. 216 (1997), 499-509. MR 99b:46029
12.: W. Rudin, Function Theory in the Unit Ball of $\mathbb{C}^{n}$ , Springer-Verlag, New York, 1980. MR 82i:32002
13.: J. H. Shi, Hadamard products of functions holomorphic on a hypersphere. Chinese Ann. Math. Ser. A 9 (1988), 49-59. (Chinese) MR 91c:32001
14.: E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970. MR 44:7280
15.: K. Stroethoff, Besov type characterization for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), 405-420. MR 90h:32012
16.: K. Stroethoff, The Bloch space and Besov spaces of analytic functions, Bull. Austral. Math. Soc. 54 (1996), 211-219. MR 97i:46046
17.: R. M. Timoney, Bloch functions in several complex variables I, Bull. London Math. Soc. 12 (1980), 241-267. MR 83b:32004
18.: R. M. Timoney, Bloch functions in several complex variables II, J. Reine Angew. Math. 319 (1980), 1-22. MR 83b:32005

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32A18, 32A37

Guangbin Ren
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China
Address at time of publication: Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Email: ren@mat.ua.pt, rengb@ustc.edu.cn

Caifeng Tu
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China
Email: tucf@ustc.edu.cn

DOI: 10.1090/S0002-9939-04-07617-8
PII: S 0002-9939(04)07617-8
Keywords: Bloch space, little Bloch space
Received by editor(s): August 16, 2001
Received by editor(s) in revised form: January 15, 2002
Posted: October 21, 2004
Additional Notes: Project supported by the NNSF of China (No. 10001030, 10471134) and the Post-doctoral Fellowship of the University of Aveiro, UID ``Matemática e Aplicações''
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2004, American Mathematical Society

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