  We obtain a Disjoint Frequent Hypercyclicity Criterion and show that it
characterizes disjoint frequent hypercyclicity for a family of unilateral
pseudo-shifts on $c_0(\mathbb{N})$ and $\ell^p(\mathbb{N})$, $1\le p <\infty$.
As an application, we characterize disjoint frequently hypercyclic weighted
shifts. We give analogous results for the weaker notions of disjoint upper
frequent and reiterative hypercyclicity. Finally, we provide counterexamples
showing that, although the frequent hypercyclicity, upper frequent
hypercyclicity, and reiterative hypercyclicity coincide for weighted shifts on
$\ell^p(\mathbb{N})$, this equivalence fails for disjoint versions of these
notions.
