Pseudo-differential operators with smooth symbols on modulation spaces

Abstract

Let  be the modulation space with parameters p, q and weight function ω₀. If ∂^αa/ω ∈ L^∞ for all α, then we prove that the pseudo-differential operator a_t(x, D) is continuous from  to . More generally, if ð”… is a translation invariant BF-space, then we prove that a_t(x, D) is continuous from M_{(ω0ω)}(ð”…) to M_(ω0)(ð”…). We use these results to establish identifications between such spaces with different weights.