Bounds on ratios of DIS structure functions from the color dipole picture

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=σL/σT of the total cross sections for longitudinally and transversely polarized photons. We further obtain bounds on the ratio of deep inelastic structure functions F2 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.