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

We study structural properties of WLq,pg,θ, which are Wiener–Lebesgue spaces with respect to a slowly varying metric g and with parameters p, q ∈ (0, ∞], θ ∈ R. For p ∈ (0, 1], we deduce Schatten-p properties for pseudo-differential operators whose symbols, together with their derivatives, obey suitable WLq,pg,θ-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.