  We calculate structure functions at small $x$ both under the assumption of a
hard singularity (a power behaviour $x^{-\lambda}, \lambda$ positive, for
$x\rightarrow 0$) or that of a soft-Pomeron dominated behaviour, also called
double scaling limit, for the singlet component. A full next to leading order
(NLO) analysis is carried for the functions $F_2, F_{\rm Glue}$ and the
longitudinal one $F_L$ in $ep$ scattering, and for $x F_3$ in neutrino
scattering. The results of the calculations are compared with data (HERA) in
the range $x\leq 0.032, 10 gev^2\leq Q^2\leq 1 500 gev^2$. We get reasonable
fits, with a chi-squared/d.o.f.$\sim 2$, for both assumptions, but none of them
gives a fully satisfactory description. The results improve substantially if
combining a soft and a hard component; in this case it is even possible to
extend the analysis, phenomenologically, to small values of $Q^2$, $0.31
gev^2\leq Q^2\leq 8.5 gev^2$, and in the $x$ range $6\times10^{-6}\lsim x \lsim
0.04$, with the same hard plus soft Pomeron hypothesis by assuming a saturating
expression for the strong coupling,
$\tilde{\alpha}_s(Q^2)=4\pi/\beta_0\log[(Q^2+\Lambda_{eff}^2)/\Lambda_{eff}^2]$
The description for low $Q^2$ implies self-consistent values for the parameters
in the exponents of $x$. One gets, for the Regge intercepts,
$\alpha_{\rho}(0)=0.48$ and $\alpha_P(0)=1.470$ [$\lambda=0.470$], in uncanny
agreement with other determinations of these parameters, in particular the
results of the large $Q^2$ fits. The fit to is so good that we may look (at
large $Q^2$) for signals of a "triple Pomeron" vertex; some evidence is found.
