  We study the tunneling density of states (TDOS) of a disordered electronic
system with Coulomb interaction on the insulating side of the Anderson
localization transition. The average TDOS shows a critical behavior at high
energies, with a crossover to a soft Coulomb gap $\Delta$ at low energies. We
demonstrate that the single-particle excitations experience a localization
transition (which belongs to the noninteracting universality class) at an
energy $E=\pm E_c$. The mobility edge $E_c$ scales with the distance
$\mu_c-\mu$ from the interacting critical point according to $E_c\propto
(\mu_c-\mu)^{\nu z}$, where $\nu$ and $z$ are the localization-length and the
dynamical critical exponents. Local TDOS shows strong fluctuations and
long-range correlations which reflect the multifractality associated with
interacting and noninteracting fixed points as well the localization of
low-energy excitations.
