On the interpolation constant for subadditive operators in Orlicz spaces
| dc.creator | Karlovich, Alexei Yu. | |
| dc.creator | Maligranda, Lech | |
| dc.date | 2007-05-02 | |
| dc.date.accessioned | 2026-07-07T07:59:09Z | |
| dc.date.available | 2026-07-07T07:59:09Z | |
| dc.description | Let $1\le p<q\le\infty$ and let $T$ be a subadditive operator acting on $L^p$ and $L^q$. We prove that $T$ is bounded on the Orlicz space $L^ϕ$, where $ϕ^{-1}(u)=u^{1/p}ρ(u^{1/q-1/p})$ for some concave function $ρ$ and \[ \|T\|_{L^ϕ\to L^ϕ}\le C\max\{\|T\|_{L^p\to L^p},\|T\|_{L^q\to L^q}\}. \] The interpolation constant $C$, in general, is less than 4 and, in many cases, we can give much better estimates for $C$. In particular, if $p=1$ and $q=\infty$, then the classical Orlicz interpolation theorem holds for subadditive operators with the interpolation constant C=1. These results generalize our results for linear operators obtained in \cite{KM01}. | |
| dc.identifier | https://arxiv.org/abs/0705.0340 | |
| dc.identifier | http://arxiv.org/abs/0705.0340 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128266 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 46E30; 46E35; 46B70; 47B65 | |
| dc.title | On the interpolation constant for subadditive operators in Orlicz spaces | |
| dc.type | text |