  The anomalous dimensions of high-twist operators in deeply inelastic
scattering ($\gamma_{2n}$) are calculated in the limit when the moment variable
$N \rightarrow 1$ (or $x_B\rightarrow 0$) and at large $Q^2$ (the double
logarithmic approximation) in perturbative QCD. We find that the value of
$\gamma_{2n}(N-1)$ in this approximation behaves as ${N_c \alpha_S \over \pi
(N-1)} n^2(1 + {\delta \over 3} (n^2-1))$ where $\delta \approx 10^{-2}$. This
implies that the contributions of the high-twist operators give rise to an
earlier onset of shadowing than was estimated before. The derivation makes use
of a Pomeron exchange approximation, with the Pomerons interacting
attractively. We find that they behave as a system of fermions.
