Möbius-invariant harmonic function spaces on the unit disc

Date

2022-03

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Source Title

Analysis Mathematica

Print ISSN

0133-3852

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Springer

Volume

48

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1

Pages

85 - 109

Language

English

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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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