Hypercontractivity for log-subharmonic functions
| dc.creator | Graczyk, Piotr | |
| dc.creator | Kemp, Todd | |
| dc.creator | Loeb, Jean-Jacques | |
| dc.creator | Zak, Tomasz | |
| dc.date | 2008-02-28 | |
| dc.date | 2008-10-20 | |
| dc.date.accessioned | 2026-07-07T10:11:09Z | |
| dc.date.available | 2026-07-07T10:11:09Z | |
| dc.description | We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on $\RR^n$ and different classes of measures: Gaussian measures on $\RR^n$, symmetric Bernoulli and symmetric uniform probability measures on $\RR$, as well as their convolutions. Surprisingly, a slightly weaker strong hypercontractivity property holds for {\em any} symmetric measure on $\RR$. For all measures on $\R$ for which we know the (SHC) holds, we prove that a log--Sobolev inequality holds in the log-subharmonic category with a constant {\em smaller} than the one for Gaussian measure in the classical context. This result is extended to all dimensions for compactly-supported measures. | |
| dc.description | 19 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0802.4260 | |
| dc.identifier | http://arxiv.org/abs/0802.4260 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171775 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47D06; 60B10; 60E15 | |
| dc.title | Hypercontractivity for log-subharmonic functions | |
| dc.type | text |