Continuity properties for modulation spaces, with applications to pseudo-differential calculus, II

We discuss continuity for weighted modulation spaces, and prove that many such spaces can be obtained in a canonical way from the corresponding standard modulation spaces. We also discuss the trace operator a-->a(0, .) acting on modulation spaces. The results are used to get inclusions between modulation spaces and Besov spaces, and proving continuity for pseudo-differential operators and Toeplitz operators.