  I deduce an inequality between the helicity and the transversity distribution
of a quark in a nucleon, at small energy scales. Then I establish, thanks to
the positivity constraint, a rigorous bound on longitudinally polarized valence
quark densities, which finds nontrivial applications to d-quarks. This, in
turn, implies a bound for the distributions of the longitudinally polarized
sea, which is probably not SU(3)-symmetric. Some model predictions and
parametrizations of quark distributions are examined in the light of these
results.
