We study general continuity properties for an increasing family of Banach spaces of classes for pseudo-differential symbols, where was introduced by J. Sjöstrand in 1993. We prove that the operators in are Schatten-von Neumann operators of order on . We prove also that and , provided . If instead , then . By modifying the definition of the -spaces, one also obtains symbol classes related to the spaces.
Nous étudions des propriétés générales de continuité pour une famille croissante d’espaces de Banach de symboles pseudo-différentiels, où 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 sur . Nous prouvons aussi que et que si . Si par contre , alors . En modifiant la définition des espaces , on obtient aussi des classes de symboles apparentés aux espaces .
Keywords: pseudo-differential operators, Weyl calculus, Schatten-von Neumann classes, admissible functions, Hölder's inequality, Young's inequality
Mot clés : opérateurs pseudo différentiels, calcul de Weyl, classes de Schatten-von Neumann, fonctions admissibles, inégalités de Hölder, inégalité de Young
@article{AIF_2001__51_5_1347_0, author = {Toft, Joachim}, title = {Subalgebras to a {Wiener} type algebra of pseudo-differential operators}, journal = {Annales de l'Institut Fourier}, pages = {1347--1383}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {5}, year = {2001}, doi = {10.5802/aif.1857}, mrnumber = {1860668}, zbl = {1027.35168}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1857/} }
TY - JOUR AU - Toft, Joachim TI - Subalgebras to a Wiener type algebra of pseudo-differential operators JO - Annales de l'Institut Fourier PY - 2001 SP - 1347 EP - 1383 VL - 51 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1857/ DO - 10.5802/aif.1857 LA - en ID - AIF_2001__51_5_1347_0 ER -
%0 Journal Article %A Toft, Joachim %T Subalgebras to a Wiener type algebra of pseudo-differential operators %J Annales de l'Institut Fourier %D 2001 %P 1347-1383 %V 51 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1857/ %R 10.5802/aif.1857 %G en %F AIF_2001__51_5_1347_0
Toft, Joachim. Subalgebras to a Wiener type algebra of pseudo-differential operators. Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1347-1383. doi : 10.5802/aif.1857. http://www.numdam.org/articles/10.5802/aif.1857/
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