Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closure properties of solutions to heat inequalities   We prove that if $u_1,u_2 : (0,\infty) \times \R^d \to (0,\infty)$ are
sufficiently well-behaved solutions to certain heat inequalities on $\R^d$ then
the function $u: (0,\infty) \times \R^d \to (0,\infty)$ given by
$u^{1/p}=u_1^{1/p_1} * u_2^{1/p_2}$ also satisfies a heat inequality of a
similar type provided $\tfrac{1}{p_1} + \tfrac{1}{p_2} = 1 + \tfrac{1}{p}$. On
iterating, this result leads to an analogous statement concerning $n$-fold
convolutions. As a corollary, we give a direct heat-flow proof of the sharp
$n$-fold Young convolution inequality and its reverse form.

21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph