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Möbius Invariant Vector‐Valued BMOA and H 1 ‐BMOA Duality of the Complex Ball
Author(s) -
Chen Zeqian,
Ouyang Caiheng
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070000168x
Subject(s) - mathematics , ball (mathematics) , pure mathematics , banach space , invariant (physics) , mathematical analysis , mathematical physics
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 L p ‐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 H 1 ‐BMOA duality theorem is proved.