  We derive bounds on ratios of deep inelastic nucleon structure functions from
the color dipole picture of high energy photon-hadron scattering. We find an
upper bound on the ratio R=sigma_L/sigma_T of the total cross sections for
longitudinally and transversely polarized photons. We further obtain bounds on
the ratio of deep inelastic structure functions F_2 taken at the same energy
but at different photon virtualities. It is shown that these bounds can be used
to constrain the range of applicability of the dipole picture.
