On the Q$^{2}$ dependence of the measured polarized structure functions

We analyse the available data on the polarized asymmetries $A_1$ for proton, neutron and deuteron targets. We use a homogeneous and updated set of unpolarized structure functions to derive $g_1$ from $A_1$, and we accurately correct for the scaling violations in order to obtain $g_1(x,Q~2)$ with the same $Q~2$ for all $x$ values. The contribution to the $Q~2$ evolution of a possible large gluon polarized density is also considered. The implications for the Ellis-Jaffe and for the Bjorken sum rules are discussed.