Pseudo-differential operators and logarithmic Schatten classes

For a Hilbert space H and positive numbers p and q, let S-p(,q) (H) stand for the class of those compact operators A on H such that Sigma(infinity)(j=1) s(j) (A)(P) vertical bar log s(j) (A)vertical bar(q) < infinity, where s(j) (A) is the jth singular value of A counted from above with multiplicity. We characterize those weights M such that for any symbol alpha is an element of S(M; Phi, Psi) the Weyl quantization of a belongs to S-p,S-q (L-2).