Möbius-invariant harmonic function spaces on the unit disc

Date
2022-03
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Source Title
Analysis Mathematica
Print ISSN
0133-3852
Electronic ISSN
Publisher
Springer
Volume
48
Issue
1
Pages
85 - 109
Language
English
Type
Article
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Abstract

We investigate and identify Möbius-invariant harmonic function spaces on the unit disc. We derive their fundamental properties and establish connections among various topologies on them. We show that the harmonic Bloch space b∞ is the “maximal” and the Besov space b−21 is the minimal invariant complete seminormed space. There is only one invariant semi-Hilbert space and it is the harmonic Dirichlet space b−22. © 2021, Akadémiai Kiadó, Budapest.

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Keywords
Harmonic Bergman - Besov space, Harmonic Bloch space, Möbius transformation, Möbius-invariant harmonic function space
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Published Version (Please cite this version)