Kaptanoğlu, Hakkı TurgayÜreyen, A. E.2022-02-102022-02-102021-12-100133-3852http://hdl.handle.net/11693/77237We 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 b1 −2 is the minimal invariant complete seminormed space. There is only one invariant semi-Hilbert space andit is the harmonic Dirichlet space b2 −2EnglishMöbius transformationMöbius-invariant harmonic function spaceHarmonic Bergman-Besov spaceHarmonic Bloch spaceArticle10.1007/s10476-021-0110-x1588-273X