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Zbl 0752.46013
Bourdaud, G.
Le calcul fonctionnel dans les espaces de Sobolev. (Functional calculus in Sobolev spaces). (French)
[J] Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1990-1991, No.IV, 4 p. (1991).

The author gives a nice brief ``tour d'horizon'' on the acting condition for the Nemytskij operator generated by an autonomous function in the Sobolev space $W\sp{m,p}(\bbfR\sp n)$ for $m\geq 0$ entire and $1\leq p\leq\infty$. This summarizes recent work of D. R. Adams, B. E. J. Dahlberg, Y. Meyer, T. Runst, W. Sickel, H. Triebel, and the author.
[J.Appell (Würzburg)]

MSC 2000:: *46E35 Sobolev spaces and generalizations
47H30 Particular nonlinear operators

Keywords: Nemytskij operator generated by a autonomous function; Sobolev space

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