Bergman spaces with small exponents (Q2710407)

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Bergman spaces with small exponents
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    Bergman spaces with small exponents (English)
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    17 February 2002
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    Bergman kernel
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    bounded symmetric domain
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    Siegel domain
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    Bloch space
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    Besov space
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    Mackey topology
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    Mackey completion
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    atomic decomposition
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    The author's abstract states: ``We give a complete proof of the characterization of the dual spaces of weighted Bergman spaces \(A^p\), \(p\in(0,1)\), of a bounded symmetric domain \(\Omega\) in \(\mathbb{C}^n\) as Besov spaces of holomorphic functions (Bloch spaces). This result was stated by K.~Zhu but there is a gap in his proof. This problem is first solved in symmetric Siegel domains of type~II and in two particular homogeneous, nonsymmetric Siegel domains of type~II. The required result is then obtained via a transfer principle from the realization of \(\Omega\) as a Siegel domain of type~II to~\(\Omega\).'' The cited paper of Zhu has been reviewed [\textit{K. Zhu}, Indiana Univ. Math. J. 44, No. 4, 1017-1031 (1995; Zbl 0853.46049)].
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