Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full Characterization of embedding relations between alpha modulation
  spaces   In this paper, we consider the embedding relations between any two $\alpha$%
-modulation spaces. Based on an observation that the $\alpha$-modulation space
with smaller $\alpha$ can be regarded as a corresponding $\alpha$% -modulation
space with larger $\alpha$, we give a complete characterization of the Fourier
multipliers between $\alpha$-modulation spaces with different $\alpha$. Then we
establish a full version of optimal embedding relations between
$\alpha$-modulation spaces. As an application, we determine that the bounded
operators commuting with translations between $\alpha$-modulation spaces are of
convolution type.

34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat