Deep inelastic scattering of leptons from nuclear targets and the BFKL Pomeron

We calculate shadowing in the process of deep inelastic interactions of leptons with nuclei in the perturbative regime of QCD. We find appreciable shadowing for heavy nuclei (e.g., Pb) in the region of a small Bjorken scaling variable ${10}^{-5}<~x<~{10}^{-3}$. This shadowing depends weakly on $Q^2$, but it may be strongly influenced, especially at $x>~{10}^{-3}$, by the existence of real parts of the forward scattering amplitudes.