  We calculate the perturbative component of the DIS structure function F_1
singlet in the Double-Logarithmic Approximation (DLA) and account at the same
time for the running QCD coupling effects. By constructing and solving
evolution equations accounting for the both x- and Q^2- evolutions, we obtain
the explicit expression for F_1 and, applying the saddle-point method,
calculate its small-x asymptotics which proves to be of the Regge form with the
intercept = 1.066. Its large value compensates for the lack of the factor 1/x
in the DLA contributions. Such fast growth at small x proves that the DLA
expressions are quite important for description of all QCD processes involving
the vacuum (Pomeron) exchanges. We also obtain that the small-x asymptotics of
F_1 depend on a single variable Q^2/x^2 and show that the small-x asymptotics
reliably represent F_1 at x = 10^{-6} or less.
