QCD expectations for the spin structure function $g_1$ in the low $x$ region

The structure function $g_1(x,Q^2)$ is analysed within the formalism based on unintegrated spin dependent parton distributions incorporating the LO Altarelli-Parisi evolution and the double $ln^2(1/x)$ resummation at low $x$. We quantitatively examine possible role of the latter for the small $x$ behaviour of the structure functions $g_1$ of the nucleon within the region which may be relevant for the possible polarized HERA measurements. We show that while the non-singlet structure function is dominated at low $x$ by ladder diagrams the contribution of the non-ladder bremsstrahlung terms is important for the singlet structure function. Predictions for the polarized gluon distribution $\Delta G(x,Q^2)$ at low $x$ are also given.