  We test the consistency of the data on the nucleon structure functions with
analyticity and the Regge asymptotics of the virtual Compton amplitude. By
solving a functional extremal problem, we derive an optimal lower bound on the
maximum difference between the exact amplitude and the dominant Reggeon
contribution for energies $\nu$ above a certain high value $\nu_h(Q^2)$.
Considering in particular the difference of the amplitudes $T_1^\inel(\nu,
Q^2)$ for the proton and neutron, we find that the lower bound decreases in an
impressive way when $\nu_h(Q^2)$ is increased, and represents a very small
fraction of the magnitude of the dominant Reggeon. While the method cannot rule
out the hypothesis of a fixed Regge pole, the results indicate that the data on
the structure function are consistent with an asymptotic behaviour given by
leading Reggeon contributions. We also show that the minimum of the lower bound
as a function of the subtraction constant $S_1^\inel(Q^2)$ provides a
reasonable estimate of this quantity, in a frame similar, but not identical to
the Reggeon dominance hypothesis.
