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 at(x, D) is continuous from to . More generally, if 𝔅 is a translation invariant BF-space, then we prove that at(x, D) is continuous from M(ω0ω)(𝔅) to M(ω0)(𝔅). We use these results to establish identifications between such spaces with different weights.
@article{1455,
title = {Pseudo-differential operators with smooth symbols on modulation spaces},
journal = {CUBO, A Mathematical Journal},
volume = {11},
year = {2009},
language = {en},
url = {http://dml.mathdoc.fr/item/1455}
}
Toft, Joachim. Pseudo-differential operators with smooth symbols on modulation spaces. CUBO, A Mathematical Journal, Tome 11 (2009) . http://gdmltest.u-ga.fr/item/1455/