Would unitarity slow down the rise of $F_2(x,Q^2)$ at $x\to 0$?
  On the grounds of the $U$--matrix form of $s$--channel unitarization, we consider constraints unitarity provides for the total cross--section of the virtual photon--induced reactions and discuss the preasymptotic nature of hadron and photon scatterings at $\sqrt{s}\leq 0.5$ TeV. 
S. M. Troshin and N. E. Tyurin