Closure properties of solutions to heat inequalities
| dc.creator | Bennett, Jonathan | |
| dc.creator | Bez, Neal | |
| dc.date | 2008-06-12 | |
| dc.date.accessioned | 2026-07-07T09:44:12Z | |
| dc.date.available | 2026-07-07T09:44:12Z | |
| dc.description | 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. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0806.2086 | |
| dc.identifier | http://arxiv.org/abs/0806.2086 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162791 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 44A35; 35K99; 52A40 | |
| dc.title | Closure properties of solutions to heat inequalities | |
| dc.type | text |