Browsing by Subject "Harmonic Bergman-Besov space"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Kelvin-Möbius-invariant harmonic function spaces on the real unit ball
    (Elsevier, 2021-05-07) Kaptanoğlu, Hakkı Turgay; Üreyen, A. E.
    We define the Kelvin-Möbius transform of a function harmonic on the unit ball of Rn and determine harmonic function spaces that are invariant under this transform. When n ≥ 3, in the category of Banach spaces, the minimal Kelvin-Möbius-invariant space is the Bergman-Besov space b1−(1+n/2) and the maximal invariant space is the Bloch space b∞(n−2)/2. There exists a unique strictly Kelvin-Möbius-invariant Hilbert space, and it is the Bergman-Besov space b2−2. There is a unique Kelvin-Möbius invariant Hardy space.
  • Thumbnail Image
    ItemOpen Access
    Möbius-invariant harmonic function spaces on the unit disc
    (Akademiai Kiado Rt., 2021-12-10) Kaptanoğlu, Hakkı Turgay; Üreyen, A. E.
    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 b1 −2 is the minimal invariant complete seminormed space. There is only one invariant semi-Hilbert space andit is the harmonic Dirichlet space b2 −2