La trivialité du calcul fonctionnel dans l’espace \(H^{3/2}(\mathbb{R}{}^ 4)\). (The functional calculus is trivial on \(H^{3/2}(\mathbb{R}{}^ 4)\)). (French) Zbl 0748.46015

Bourdaud, Gérard

C. R. Acad. Sci., Paris, Sér. I 314, No. 3, 187-190 (1992).

Let \(G\) be a real-variable function such that, for each \(f\in H^{3/2}(\mathbb{R}^ n)\) (\(n\geq 4\)), we have \(G(f)\in H^{3/2}(\mathbb{R}^ n)\); then there exists a constant \(c\) such that \(G(t)=ct\), for all \(t\). This result is also true for the Besov and Triebel-Lizorkin spaces, when \(s=1+(1/p)\) and \(1\leq p<n-1\).

Reviewer: G.Bourdaud

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47A60	Functional calculus for linear operators

Keywords:

Besov spaces; Triebel-Lizorkin spaces