Embedding of normed spaces in $L_p, p< 0$.

If $0 < p\le 2$ and $(X_t)$ is a symmetric p-stable process then $T(f) = \int_0^1 f(t)dX_t$ is an isometric embedding of $L_p[0,1]$ into $L_q(\Omega)$ for each $ 0\le q < p\le 2$. We extend the concept of embedding of a normed space in $L_q$ to negative values of $q$ and show several applications to convex geometry.