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Le calcul fonctionnel dans les espaces de Sobolev. (Functional calculus in Sobolev spaces). (French) Zbl 0752.46013

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 \(W^{m,p}(\mathbb{R}^ n)\) 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.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Full Text: Numdam EuDML