Continuity of composition operators in Sobolev spaces

Bourdaud, Gérard; Moussai, Madani

doi:10.1016/j.anihpc.2019.07.002

Bourdaud, Gérard ¹ ; Moussai, Madani ²

¹ Université de Paris, I.M.J. - P.R.G., Case 7012, 75205 Paris Cedex 13, France
² Laboratory of Functional Analysis and Geometry of Spaces, M. Boudiaf University of M'Sila, 28000 M'Sila, Algeria

Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 2053-2063.

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Résumé

We prove that all the composition operators $T_{f} (g) : = f \circ g$ , which take the Adams-Frazier space $W_{p}^{m} \cap {\dot{W}}_{m p}^{1} (R^{n})$ to itself, are continuous mappings from $W_{p}^{m} \cap {\dot{W}}_{m p}^{1} (R^{n})$ to itself, for every integer $m \geq 2$ and every real number $1 \leq p < \infty$ . The same automatic continuity property holds for Sobolev spaces $W_{p}^{m} (R^{n})$ for $m \geq 2$ and $1 \leq p < \infty$ .

MR Zbl

DOI : 10.1016/j.anihpc.2019.07.002

Classification : 46E35, 47H30
Mots-clés : Composition operators, Sobolev spaces

Affiliations des auteurs :

Bourdaud, Gérard ¹ ; Moussai, Madani ²

¹ Université de Paris, I.M.J. - P.R.G., Case 7012, 75205 Paris Cedex 13, France
² Laboratory of Functional Analysis and Geometry of Spaces, M. Boudiaf University of M'Sila, 28000 M'Sila, Algeria

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     title = {Continuity of composition operators in {Sobolev} spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2053--2063},
     publisher = {Elsevier},
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     zbl = {1456.46028},
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Bourdaud, Gérard; Moussai, Madani. Continuity of composition operators in Sobolev spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 2053-2063. doi : 10.1016/j.anihpc.2019.07.002. http://www.numdam.org/articles/10.1016/j.anihpc.2019.07.002/

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