Second derivative test for isometric embeddings in $L_p$

Details Second derivative test for isometric embeddings in $L_p$ Second derivative test for isometric embeddings in $L_p$

1997-02-06

arxiv.org/abs/math/9702211v1

Mathematics

Functional Analysis

Scientific paper

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

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