\quad
a\in M^{p,p}, \ p\in (0,2],$$ i.e. still holds after $[1,2]$ is replaced by the larger interval $(0,2]$. Furthermore, we prove that $'$ is sharp in the sense that any modulation space (with trivial weight), and not contained in $M^{p,p}({\mathbf R^{2d}})$, contains symbols, whose corresponding pseudo-differential operators fail to belong to ${\mathscr I}_p$ (cf. Theorem \[SchattenConverse\]).

In Section \[sec3\] we also deduce general continuity results for pseudo-differential operators with symbols in modulation spaces. In particular, is extended in Theorem \[thmOpCont\] extend in several ways, and as special case, and are extended into $$\begin{gathered}
\tag*{(\ref{ModCont1})$'$}
{\operatorname{Op}}(a) \, :\, M^{p_1,q_1}\to M^{p_1,q_1}
\\[1ex]
\text{when} \quad
a\in M^{\infty ,q},\ p_1,q_1\in [q,\infty ],\ q\in (0,1],\end{gathered}$$ and $$\tag*{(\ref{ModCont1B})$'$}
{\operatorname{Op}}(a) \, :\, M^{\infty ,\infty }\to M^{q,q} 
\quad  \text{when} \quad
a\in M^{q ,q},\ q\in (0,1].$$

In Section \[sec4\] we apply $'$ to deduce Schatten-von Neumann properties for pseudo-differential operators with symbols in $S(m,g)$ in H[ö]{}rmander-Weyl calculus. In particular we show that the sufficiency part of still holds for $p\in (0,1]$ (cf. Theorem \[thm:WeylHorm1\]). That is, for suitable $m$ and $g$, we have $${\{ \, {\operatorname{Op}}_t(a)\, ;\, a\in S(m,g)\, \} }\subseteq {\mathscr I}_p
\quad \text{when} \quad
m\in L^p.$$

An important part behind the analysis concerns Theorem \[factorizationprop\], which in 