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The Möbius boundedness of the space Qp

Part of: Special classes of linear operators Holomorphic functions of several complex variables

Published online by Cambridge University Press:  09 April 2009

Hu Pengyan ,
Shi Jihuai  and
Zhang Wenjun
Hu Pengyan
Affiliation:
Department of Mathematics, Normal College of Shenzhen University, Shenzhen, Guangdong 518060, P. R. China e-mail: [email protected]
Shi Jihuai
Affiliation:
Department of Mathematics, University of Science, and Technology of China, Hefei, Anhui 230026, P. R. China
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Abstract

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In this note, a characterization of the Möbius invariant space Qp for the range 1 - 1/n lt; p ≤ 1 is given. As a special case p = 1, we get the Möbius boundedness of BMOA in the space H2. This extends the corresponding result for 1-dimension.

Keywords

Möbius invariant spaceDirichiet type spaceinvariant volume measuretangent gradient

MSC classification

Secondary: 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 373 - 378
Copyright
Copyright © Australian Mathematical Society 1999

References

[ALXZ]Aulaskari, R., Lappan, P., Xiao, J. and Zhao, R., ‘On α-Bloch spaces and multipliers of Dirichlet spaces’, J. Math. Anal. Appl. 209 (1997), 103–121.CrossRefGoogle Scholar
[Ba]Baernstein, A. II, Analytic functions of bounded mean oscillation, aspects of contemporary complex analysis (Academic Press, New York, 1980) pp. 3–36.Google Scholar
[Je]Jevtié, M., ‘On the Carleson measure characterization of BMO functions on the unit sphere’, Proc. Amer. Math. Soc. 123 (1995), 3371–3377.CrossRefGoogle Scholar
[JP]Jevtić, M. and Pavlović, M., ‘On ℳ’-harmonic Bloch space’, Proc. Amer Math. Soc. 123 (1995), 1385–1392.Google Scholar
[OYZ]Ouyang, C., Yang, W. and Zhao, R., ‘Möbius invariant Qp spaces associated with the Green's function on the unit ball of Pacific J. Math. (to appear).Google Scholar
[Ru]Rudin, W., Function theory in the unit ball of (Springer, New York, 1980).CrossRefGoogle Scholar
[St]Stoll, M., Invariant potential theory in the unit ball of , London Math. Soc. Lecture Notes 199 (Cambridge Univ. Press, New York, 1994).CrossRefGoogle Scholar