Quasi-Banach Schatten-von Neumann properties in Weyl-H\"ormander calculus
Abstract
We study structural properties of Wiener-Lebesgue spaces with respect to a slowly varying metrics and certain Lebesgue parameters. For p∈ (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-H\"ormander calculus. Finally, we apply our results to global-type SG and Shubin pseudo-differential operators.
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