Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of probability measure with finite moment and an
  application to the Boltzmann equation   We characterize probability measure with finite moment of any order in terms
of the symmetric difference operators of their Fourier transforms. By using our
new characterization, we prove the continuity $f(t,v)\in C((0,
\infty),L^1_{2k-2 +\alpha})$, where $f(t, v)$ stands for the density of unique
measure-valued solution $(F_t)_{t\ge0}$ of the Cauchy problem for the
homogeneous non-cutoff Boltzmann equation, with Maxwellian molecules,
corresponding to a probability measure initial datum $F_0$ satisfying \[ \int
|v|^{2k-2+\alpha} dF_0(v) < \infty, 0\leq \alpha < 2,k= 2, 3, 4,\cdots \]
provided that $F_0$ is not a single Dirac mass.

5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph