Kaptanoğlu, Hakkı Turgay2023-02-172023-02-172022-030133-3852http://hdl.handle.net/11693/111513We 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.EnglishHarmonic Bergman - Besov spaceHarmonic Bloch spaceMöbius transformationMöbius-invariant harmonic function spaceArticledoi.org/10.1007/s10476-021-0110-x