  If $E=\{e_i\}$ and $F=\{f_i\}$ are two 1-unconditional basic sequences in
$L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some $1\le r<p\le 2$, then
the space of matrices $\{a_{i,j}\}$ with norm
  $\|\{a_{i,j}\}\|_{E(F)}=\big\|\sum_k \|\sum_l a_{k,l}f_l\|e_k\big\|$ embeds
into $L_1$. This generalizes a recent result of Prochno and Sch\"utt.
