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Fonctions qui opèrent sur les espaces de Sobolev. (Functions that operate on Sobolev spaces). (French) Zbl 0737.46011

Les auteurs cherchent à étendre des résultats concernant les fonctions \(F\) de la variable réelle opèrant dans un ensemble.
Ils montrent que si \(p\) et \(q\in [1,+\infty]\), \(s\in ]0,{1 \over p}[\), \(F: t\in \mathbb{R}\to | t|\) opère dans l’espace de Besov \(B_ p^{s,q}(\mathbb{R})\) et que l’on a plus prècisément: \(\exists c\|| f |\|_{B_ p^{s,q}}\leq c\| f\|_{B_ p^{s,q}}\) (th. 2), et donnent un contre exemple lorsque \(p,q\in [1,+\infty]\) et \(s\geq 1+{1 \over p}\).

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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