Weyl product algebras and modulation spaces. (English) Zbl 1137.46017
The authors investigate algebraic properties of the Weyl product on modulation spaces and generalize most of the existing results on necessary and sufficient conditions for modulation spaces to be algebras under this product. They assume weaker conditions on polynomially moderated weight functions \(\omega_j\) for \(j=0,1,2\) which satisfy the inequality \(\omega_0(X,Y)\leq C\omega_1(X-Y+Z,Z)\omega_2(X+Z,Y-Z)\), for \(X,Y,Z\in{\mathbb R}^{2d}\) for some constant \(C>0\). However, submultiplicative weights are not permitted. The last section contains some remarks on the Wiener property and modulation spaces.
Reviewer: Rémi Vaillancourt (Ottawa)
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 47G30 | Pseudodifferential operators |
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