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Analytic \(Q_{\log,p}\) spaces. (English) Zbl 1435.30146

Summary: As a novel bridge between the Dirichlet space \({\mathcal{D}} \), the John-Nirenberg space \(\mathcal{BMOA} \), and the Bloch space \({\mathcal{B}}\) on the unit disk, the Moebius invariant analytic function space \(Q_{\log,p}\) founded directly on a Moebius invariant isoperimetry is discovered in accordance with the Moebius invariant inclusion chain \({\mathcal{H}}^\infty \subsetneq \mathcal{BMOA}\subsetneq{\mathcal{B}} \), where \({\mathcal{H}}^\infty\) is the Hardy algebra of all bounded analytic functions on the unit disk.

MSC:

30H05 Spaces of bounded analytic functions of one complex variable
30H25 Besov spaces and \(Q_p\)-spaces
30H80 Corona theorems
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