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

By J. Toft. 2004

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Changes of variables in modulation and Wiener amalgam spaces (2008, background): “2 In [33] it was proved that ei|D | 2 is bounded on each modulation space, and in [3] it was shown that for 0 ≤ α ≤ 2, the operators ei|D | are bounded on the modulation spaces Mp,q (R ), 1 ≤ p, q ≤ ∞ (for the definition of Mp,q (R ) see Remark 3.”
The dilation property of modulation spaces and their inclusion relation with Besov spaces (2006, background): “Now we are in a situation to start showing fundamental properties of the modulation spaces, in order to apply them for many other problems.”
Sharpness of some properties of Wiener amalgam and modulation spaces (2008, positive): “This study was widely carried out in [17] (see also [5, 20]) in the case of modulation spaces M.”