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  • Author: Winfried Sickel x
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Abstract

Let G: ℝ → ℝ be a continuous function. Denote by TG the corresponding composition operator which sends ƒ to G(ƒ). Then we investigate necessary and sufficient conditions on the parameters s, p, q, r and on the function G such that an inclusion like

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is true. Here F s p, q denotes a space of Triebel-Lizorkin type and W m p denotes a Sobolev space, respectively. Necessary and sufficient conditions for such an inclusion to hold will be given in cases G(t) = t k, k ∈ ℕ, G(t) = |t|μ, G(t) = t|t|μ - 1, μ > 1, GC 0 , and G a periodic C -function.

Abstract

Let G: ℝ → ℝ be a continuous function. Denote by TG the corresponding composition operator which sends ƒ to G(ƒ). Then we investigate consequences for the parameters s, p, and r of the inclusion

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Here B s p, q denotes a Besov space.