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MÖBIUS INVARIANT VECTOR-VALUED BMOA AND H1-BMOA DUALITY OF THE COMPLEX BALL

Published online by Cambridge University Press:  19 March 2001

ZEQIAN CHEN  and
CAIHENG OUYANG
ZEQIAN CHEN
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071, China; [email protected]
CAIHENG OUYANG
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071, China; [email protected]
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Abstract

Two classes of vector-valued BMOA spaces are defined, in the complex ball and on the complex sphere, respectively. In the case of the complex sphere, vector measures are involved, since the argument in the scalar setting is not appropriate. Several properties (the Lp-equivalent norm theorem, exponential decay, the Baernstein theorem, and so on) of BMOA in the complex ball are extended to the Banach space setting. The two classes of BMOA spaces are proved to be isomorphic; in particular, the corresponding John–Nirenberg exponential decay is shown. Finally, the vector-valued H1-BMOA duality theorem is proved.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 159 - 176
Copyright
The London Mathematical Society 2001

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Footnotes

Project supported by the National Natural Science Foundation of China.