Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional inequalities related to the Rogers-Shephard inequality   For a real-valued non-negative and log-concave function we introduce a notion
of difference function; the difference function represents a functional analog
on the difference body of a convex body. We prove a sharp inequality which
bounds the integral of the difference function from above in terms of the
integral of the function itself, and we characterize equality conditions. The
investigation is extended to an analogous notion of difference function for
$\alpha$-concave functions, with $\alpha$ smaller than zero. In this case also,
we prove an upper bound for the integral of the $\alpha$-difference function of
a function in terms of the integral of the function itself; the bound is proved
to be sharp when $\alpha$ is equal to minus infinity and in the one dimensional
case.

4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys