We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

The modulation spaces M m (R ) quantify the time-frequency concentration of functions and distributions. The first main result of this paper proves embeddings of certain modulation spaces into VMO, the space of functions with vanishing mean oscillation. The second main result proves that the Zak transform maps certain modulation spaces on R into modulation spaces on R. These two results allow u...

The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m-term nonlinear approximation with brushlet bases, and give complete characterizations of the associated approximation spaces in terms of α-mo...

Exploiting continuity properties of Fourier multipliers on modulation spaces and Wiener amalgam spaces, we study the Cauchy problem for the NLW equation. Local wellposedness for rough data in modulation spaces and Wiener amalgam spaces is shown. The results formulated in the framework of modulation spaces refine those in [3]. The same arguments may apply to obtain local wellposedness for the NL...

The (classical) modulation spaces, as introduced by Feichtinger during the 80’s, consist of all tempered distributions whose short-time Fourier transforms (STFT) have finite mixed (weighted) Lebesgue norm. By choosing the Lebesgue parameters and weight functions in appropriate ways, one may quantify the degrees of asymptotic decay and singularity of the distributions in a ”detailed way”. A majo...

In this paper, we consider the embedding relations between any two α-modulation spaces. Based on an observation that the α-modulation space with smaller α can be regarded as a corresponding α-modulation space with larger α, we give a complete characterization of the Fourier multipliers between α-modulation spaces with different α. Then we establish a full version of optimal embedding relations ...

In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of modulation and Wiener amalgam spaces and, as a consequence, we obtain several versions of local and global Beurling–Helson type theorems. We also establish a number ...

In this article, we consider the Cauchy problem for dispersive equations in α-Modulation spaces. For this purpose, we find a method for estimating uk in α-modulation spaces when k is not an integer, and develop a Strichartz estimate in M p,q which is based on semigroup estimates. In the local case, we that the domain of p is independent of α, which is also the case in the Modulation spaces and ...