Subalgebras to a Wiener type algebra of pseudo-differential operators
[Sous-algèbres de Wiener d'opérateurs pseudo différentiels]
Annales de l'Institut Fourier, Tome 51 (2001) no. 5, pp. 1347-1383.

We study general continuity properties for an increasing family of Banach spaces Swp of classes for pseudo-differential symbols, where Sw=Sw was introduced by J. Sjöstrand in 1993. We prove that the operators in Op(Swp) are Schatten-von Neumann operators of order p on L2. We prove also that Op(Swp)Op(Swr)Op(Swr) and Swp·SwqSwr, provided 1/p+1/q=1/r. If instead 1/p+1/q=1+1/r, then Swpw*SwqSwr. By modifying the definition of the Swp-spaces, one also obtains symbol classes related to the S(m,g) spaces.

Nous étudions des propriétés générales de continuité pour une famille croissante d’espaces de Banach Swp de symboles pseudo-différentiels, où Sw=Sw a été introduit par J. Sjöstrand en 1993. Nous montrons que les opérateurs associés à ces symboles sont des opérateurs de Schatten-von Neumann d’ordre p sur L2. Nous prouvons aussi que Op(Swp)Op(Swr)Op(Swr) et que Swp·SwqSwr si 1/p+1/q=1/r. Si par contre 1/p+1/q=1+1/r, alors Swpw*SwqSwr. En modifiant la définition des espaces Swp, on obtient aussi des classes de symboles apparentés aux espaces S(m,g).

DOI : 10.5802/aif.1857
Classification : 35S05, 47B10, 47B33, 42B99, 28E99
Keywords: pseudo-differential operators, Weyl calculus, Schatten-von Neumann classes, admissible functions, Hölder's inequality, Young's inequality
Mots-clés : opérateurs pseudo différentiels, calcul de Weyl, classes de Schatten-von Neumann, fonctions admissibles, inégalités de Hölder, inégalité de Young

Toft, Joachim 1

1 Blekinge Technical University, Department of Mathematics, IHN, 371-79 Karlskrona (Suède)
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Toft, Joachim. Subalgebras to a Wiener type algebra of pseudo-differential operators. Annales de l'Institut Fourier, Tome 51 (2001) no. 5, pp. 1347-1383. doi : 10.5802/aif.1857. https://www.numdam.org/articles/10.5802/aif.1857/

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