  We consider a system of two-dimensional electrons strongly localized by
disorder. Interactions create a gap in the average tunneling density of states
$\nu(E)$ at energies, E, close to the Fermi level. We derive a system of
self-consistent equations for the correlators of local densities of occupied
and empty states. When either the interactions are screened by the gate or the
temperature, T, is high enough, so that the Coulomb gap is shallow, the
perturbative solution of the system yields analytical expressions for the
interaction-induced correction $\delta\nu(E)$ and the level-level correlator.
We show that even with short-range interactions, $\delta\nu (E)$ exhibits a
singular energy dependence at T=0. We also demonstrate that at high T this
energy dependence is a universal function of the the ratio $E/T$. Regarding the
level correlations, we trace how the correlator falls off as a function of
spatial and energy separation between the levels. We also trace how the
correlations vanish with increasing T. Our most noticeable observation is that
for two close energies the correlator changes sign from positive (attraction)
at small distances to negative (repulsion) at large distances.
