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The structure function $g_1(x,Q^2)$ is analysed within the formalism based onunintegrated spin dependent parton distributions incorporating the LOAltarelli-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 regionwhich may be relevant for the possible polarized HERA measurements. We showthat while the non-singlet structure function is dominated at low $x$ by ladderdiagrams the contribution of the non-ladder bremsstrahlung terms is importantfor the singlet structure function. Predictions for the polarized gluondistribution $\Delta G(x,Q^2)$ at low $x$ are also given.Comment: 24 pages, latex, 7 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

QCD expectations for the spin structure function<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>in the low<i>x</i>region

QCD expectations for the spin structure functiong1in the lowxregion