Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces.

Let M(ω)p,q be the modulation space with parameters p, q and weight function ω. We prove that if t ∈ R, p, pj, q, qj ∈ [1, ∞], ω1, ω2 and ω are appropriate, and a ∈ M(ω)p,q, then the pseudo-differential operator at(x,D) is continuous from M(ω)p1,q1 to M(ω)p2,q2. If in addition pj = qj = 2, then we establish necessary and sufficient conditions on p and q in order to at(x,D) should be a Schatten-von Neumann operator of certain order. [ABSTRACT FROM AUTHOR]