Quasi-Banach Schatten-von Neumann properties in Weyl-Hörmander calculus

Abstract

We study structural properties of Wiener-Lebesgue spaces with respect to a slowly varying metrics and certain Lebesgue parameters. For $p\in (0,1]$, we deduce Schatten-$p$ properties for pseudo-differential operators whose symbols, together with their derivatives, obey suitable Wiener-Lebesgue-boundedness conditions. Especially, we perform such investigations for the Weyl-Hörmander calculus. Finally, we apply our results to global-type SG and Shubin pseudo-differential operators.

21 pages. This is the first version. Some changes might be performed in the next versions