  We consider two operator space versions of type and cotype, namely
$S_p$-type, $S_q$-cotype and type $(p,H)$, cotype $(q,H)$ for a homogeneous
Hilbertian operator space $H$ and $1\leq p \leq 2 \leq q\leq \infty$,
generalizing "$OH$-cotype 2" of G. Pisier. We compute type and cotype of some
Hilbertian operator spaces and $L_p$ spaces, and we investigate the
relationship between a homogeneous Hilbertian space $H$ and operator spaces
with cotype $(2,H)$. As applications we consider operator space versions of
generalized little Grothendieck's theorem and Maurey's extension theorem in
terms of these new notions.
