Sharp constants related to the triangle inequality in Lorentz spaces
| dc.creator | Barza, Sorina | |
| dc.creator | Kolyada, Viktor | |
| dc.creator | Soria, Javier | |
| dc.date | 2007-09-05 | |
| dc.date.accessioned | 2026-07-07T08:27:45Z | |
| dc.date.available | 2026-07-07T08:27:45Z | |
| dc.description | We study the Lorentz spaces $L^{p,s}(R,μ)$ in the range $1<p<s\le \infty$, for which the standard functional $$ ||f||_{p,s}=(\int_0^\infty (t^{1/p}f^*(t))^s\frac{dt}{t})^{1/s} $$ is only a quasi-norm. We find the optimal constant in the triangle inequality for this quasi-norm, which leads us to consider the following decomposition norm: $$ ||f||_{(p,s)}=\inf\bigg\{\sum_{k}||f_k||_{p,s}\bigg\}, $$ where the infimum is taken over all finite representations $f=\sum_{k}f_k. $ We also prove that the decomposition norm and the dual norm $$ ||f||_{p,s}'= \sup\left\{\int_R fg dμ: ||g||_{p',s'}=1\right\} $$ agree for all values $p,s>1$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0709.0647 | |
| dc.identifier | http://arxiv.org/abs/0709.0647 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137374 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 46E30, 46B25 | |
| dc.title | Sharp constants related to the triangle inequality in Lorentz spaces | |
| dc.type | text |