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

function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...