  We present a comprehensive study of high-energy double logarithms in
inclusive DIS. They appear parametrically as alpha_s^n ln^{2n-k} x at the n-th
order in perturbation theory in the splitting functions for the parton
evolution and the coefficient functions for the hard scattering process, and
represent the leading corrections at small $x$ in the flavour non-singlet case.
We perform their resummation, in terms of modified Bessel functions, to all
orders in full QCD up to NNLL accuracy, and partly to N^3LL and beyond in the
large-n_c limit, and provide fixed-order expansions up to five loops. In the
flavour-singlet sector, where these double logarithms are sub-dominant at small
x compared to single-logarithmic alpha_s^n x^{-1} ln^{n-k} x BFKL
contributions, we construct fixed-order expansions up to five loops at NNLL
accuracy in full QCD. The results elucidate the analytic small-x structure
underlying inclusive DIS results in fixed-order perturbation theory and provide
important information for present and future numerical and analytic
calculations of these quantities.
