  The unpolarized, helicity and transversity distributions of quarks in the
proton are calculated in the overlap representation of light-cone wavefunctions
truncated to the lowest order Fock-space components with three valence quarks.
The three distributions at the hadronic scale satisfy an interesting relation
consistent with the Soffer inequality. Results are derived in a relativistic
quark model including radiative corrections up to the next-to-leading order.
Predictions for the double transverse-spin asymmetry in Drell-Yan dilepton
production initiated by proton-antiproton collisions are presented. Asymmetries
of about 20-30% are found in the kinematic conditions of the PAX experiment.
