Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On improvement of summability properties in nonautonomous Kolmogorov
  equations   Under suitable conditions, we obtain some characterization of
supercontractivity, ultraboundedness and ultracontractivity of the evolution
operator $G(t,s)$ associated to a class of nonautonomous second order parabolic
equations with unbounded coefficients defined in $I\times\R^d$, where $I$ is a
right-halfline. For this purpose, we establish an Harnack type estimate for
$G(t,s)$ and a family of logarithmic Sobolev inequalities with respect to the
unique tight evolution system of measures $\{\mu_t: t \in I\}$ associated to
$G(t,s)$. Sufficient conditions for the supercontractivity, ultraboundedness
and ultracontractivity to hold are also provided.

26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex