  We present all-order results for the highest three large-x logarithms of the
splitting functions P_qg and P_gq and of the coefficient functions C_phi,q,
C_2,g and C_L,g for structure functions in Higgs- and gauge-boson exchange DIS
in massless perturbative QCD. The corresponding coefficients have been derived
by studying the unfactorized partonic structure functions in dimensional
regularization independently in terms of their iterative structure and in terms
of the constraints imposed by the functional forms of the real- and
virtual-emission contributions together with their Kinoshita--Lee-Nauenberg
cancellations required by the mass-factorization theorem. The numerical
resummation corrections are small for the splitting functions, but partly very
large for the coefficient functions. The highest two (three for C_L,g)
logarithms can be resummed in a closed form in terms of new special functions
recently introduced in the context of the resummation of the leading logarithms
