  We prove two-sided Chevet-type inequalities for independent symmetric Weibull
random variables with shape parameter $r\in[1,2]$. We apply them to provide
two-sided estimates for operator norms from $\ell_p^n$ to $\ell_q^m$ of random
matrices $(a_ib_jX_{i,j})_{i\le m, j\le n}$, in the case when $X_{i,j}$'s are
iid symmetric Weibull variables with shape parameter $r\in[1,2]$ or when $X$ is
an isotropic log-concave unconditional random matrix. We also show how these
Chevet-type inequalities imply two-sided bounds for maximal norms from
$\ell_p^n$ to $\ell_q^m$ of submatrices of $X$ in both Weibull and log-concave
settings.
