Bergman spaces with small exponents (Q2710407)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Bergman spaces with small exponents |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bergman spaces with small exponents |
scientific article |
Statements
Bergman spaces with small exponents (English)
0 references
17 February 2002
0 references
Bergman kernel
0 references
bounded symmetric domain
0 references
Siegel domain
0 references
Bloch space
0 references
Besov space
0 references
Mackey topology
0 references
Mackey completion
0 references
atomic decomposition
0 references
0.96645194
0 references
0.91571426
0 references
0.91558045
0 references
0.9078201
0 references
0 references
0 references
0.9024078
0 references
0 references
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)].
0 references