Weyl product algebras and modulation spaces

We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions ω we prove that M p,q (ω) is an algebra under the Weyl product if p ∈ [1,∞] and 1 q min(p,p ). For the remaining cases p ∈ [1,∞] and min(p,p ) < q ∞ we show that the unweighted spaces Mp,q are not algebras under the Weyl product. © 2007 Elsevier Inc. All rights reserved.