Browsing by Subject "Atomic decomposition"

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    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.
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    ItemOpen Access
    Precise inclusion relations among Bergman-Besov and Bloch-Lipschitz spaces and H∞ on the unit ball of CN
    (Wiley-VCH Verlag, 2018) Kaptanoğlu, Hakkı Turgay; Üreyen, A. E.
    We describe exactly and fully which of the spaces of holomorphic functions in the title are included in which others. We provide either new results or new proofs. More importantly, we construct explicit functions in each space that show our relations are strict and the best possible. Many of our inclusions turn out to be sharper than the Sobolev imbeddings.