Abstract
We characterize Triebel‐Lizorkin spaces with positive smoothness on ℝn, obtained by different approaches. First we present three settings associated to definitions by differences, Fourier‐analytical methods and subatomic decompositions. We study their connections and diversity, as well as embeddings between these spaces and into Lorentz spaces. Secondly, relying on previous results obtained for Besov spaces , we determine their growth envelopes for 0≺p≺∞, 0≺q ≤ ∞, s≻0, and finally discuss some applications.
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