Schatten classes for Toeplitz operators with Hilbert space windows on modulation spaces

We prove that if ω, ω1, ω2, v1, v2 are appropriate, , j=1,2, and ωa∈Lp, then the Toeplitz operator Tph1,h2(a) from to belongs to the Schatten–von Neumann class of order p. From this property we prove convolution properties between weighted Lebesgue spaces and Schatten–von Neumann classes of symbols in pseudo-differential calculus.