  In the framework of the $k_T$-factorization approach, the production of
Upsilon mesons at the Fermilab Tevatron is considered, and the comparisions of
calculated $p_T$-distributions and spin alignment parameter $\alpha$ with the
D0 experimental data are shown. We argue that measuring the double cross
section and the polarization of upsilonium states can serve as a crucial test
discriminating two competing theoretical approaches to parton dynamics in QCD.
