The paper deals with inclusion relations between s(p) and H-s(p). Here s(p) is the set of all a is an element ofJ such that the Weyl operator a(w) (x, D) is a Schatten-von Neumann operator on L-2 to the order p is an element of [1, infinity], and H-s(p) is the Sobolev space of distributions with s derivatives in L-p. At the same time we compute the trace norm for a(w) (x, D), when a is an arbitrary Gauss function.