  We define, within the Schr\"odinger functional (SF) scheme, the matrix
elements of the twist-2 operators corresponding to the first two moments of
non-singlet parton density, and the first moment of singlet parton densities.
We perform a lattice one-loop calculation that fixes the relation between the
SF scheme and other common schemes and shows the main source of lattice
artefacts. Few remarks on the improvement case are added.
