  We prove that the class of Banach function lattices in which all relatively
weakly compact sets are equi-integrable sets (i.e. spaces satisfying the
Dunford-Pettis criterion) coincides with the class of 1-disjointly homogeneous
Banach lattices. A new examples of such spaces are provided. Furthermore, it is
shown that Dunford-Pettis criterion is equivalent to de la Vallee Poussin
criterion in all rearrangement invariant spaces on the interval. Finally, the
results are applied to characterize weakly compact pointwise multipliers
between Banach function lattices.
