Continuity of composition operators in Sobolev spaces

Bourdaud, Gérard; Moussai, Madani

doi:10.1016/j.anihpc.2019.07.002

¹Université de Paris, I.M.J. - P.R.G., Case 7012, 75205 Paris Cedex 13, France
²Laboratory 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

Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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
Keywords: 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

@article{AIHPC_2019__36_7_2053_0,
     author = {Bourdaud, G\'erard and Moussai, Madani},
     title = {Continuity of composition operators in {Sobolev} spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2053--2063},
     year = {2019},
     publisher = {Elsevier},
     volume = {36},
     number = {7},
     doi = {10.1016/j.anihpc.2019.07.002},
     mrnumber = {4020533},
     zbl = {1456.46028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.07.002/}
}

TY  - JOUR
AU  - Bourdaud, Gérard
AU  - Moussai, Madani
TI  - Continuity of composition operators in Sobolev spaces
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2019
SP  - 2053
EP  - 2063
VL  - 36
IS  - 7
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.07.002/
DO  - 10.1016/j.anihpc.2019.07.002
LA  - en
ID  - AIHPC_2019__36_7_2053_0
ER  -

%0 Journal Article
%A Bourdaud, Gérard
%A Moussai, Madani
%T Continuity of composition operators in Sobolev spaces
%J Annales de l'I.H.P. Analyse non linéaire
%D 2019
%P 2053-2063
%V 36
%N 7
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.07.002/
%R 10.1016/j.anihpc.2019.07.002
%G en
%F AIHPC_2019__36_7_2053_0

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

Cité par Sources :

Parcourir par

Geodesic

Parcourir par