Second derivative test for isometric embeddings in $L_p$
| dc.creator | Koldobsky, Alexander | |
| dc.date | 1997-02-06 | |
| dc.date.accessioned | 2026-07-07T09:15:43Z | |
| dc.date.available | 2026-07-07T09:15:43Z | |
| dc.description | An old problem of P. Levy is to characterize those Banach spaces which embed isometrically in $L_p.$ We show a new criterion in terms of the second derivative of the norm. As an application, we show that if $M$ is a twice differentiable Orlicz function with $M'(0)=M''(0)=0$ then the $n$-dimensional Orlicz space $\ell_M^n,\ n\ge 3,$ does not embed isometrically in $L_p$ with $0<p\le 2.$ These results generalize and clear up the recent solution to the 1938 Schoenberg's problem on positive definite functions. | |
| dc.identifier | https://arxiv.org/abs/math/9702211 | |
| dc.identifier | http://arxiv.org/abs/math/9702211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153111 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B04 | |
| dc.title | Second derivative test for isometric embeddings in $L_p$ | |
| dc.type | text |