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Conditions on composition operators which map a space of Triebel-Lizorkin type into a Sobolev space. The case 1 < s < n/p. II
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Winfried Sickel
Published/Copyright:
March 2, 2009
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
is true. Here Fsp, q denotes a space of Triebel-Lizorkin type and Wmp denotes a Sobolev space, respectively. Necessary and sufficient conditions for such an inclusion to hold will be given in cases G(t) = tk, k ∈ ℕ, G(t) = |t|μ, G(t) = t|t|μ - 1, μ > 1, G ∈ C0∞, and G a periodic C∞-function.
Received: 1996-06-25
Revised: 1997-03-20
Published Online: 2009-03-02
Published in Print: 1998-03-11
© Walter de Gruyter
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Articles in the same Issue
- On Weiss' geometric characterization of the Rudvalis simple group
- Filtrations in feedback synthesis: Part I – Systems and feedbacks
- On twists of cuspidal representations of GL(2)
- Conditions on composition operators which map a space of Triebel-Lizorkin type into a Sobolev space. The case 1 < s < n/p. II
- Smooth unions of Butler groups
- Nonhenselian valuation domains and the Krull–Schmidt Property for torsion-free modules
Articles in the same Issue
- On Weiss' geometric characterization of the Rudvalis simple group
- Filtrations in feedback synthesis: Part I – Systems and feedbacks
- On twists of cuspidal representations of GL(2)
- Conditions on composition operators which map a space of Triebel-Lizorkin type into a Sobolev space. The case 1 < s < n/p. II
- Smooth unions of Butler groups
- Nonhenselian valuation domains and the Krull–Schmidt Property for torsion-free modules
