Nonleading logarithmic corrections to the Sudakov form factor in quantum chromodynamics

One- and two-loop corrections to the vertex functions and the quark and gluon propagators are investigated in quantum chromodynamics. It is shown that in deep inelastic processes the running coupling constant ..cap alpha../sub s/ is a function of the transverse momentum of the emitted gluons. Nonleading corrections of the form ..cap alpha../sup n//sub s/ log/sup 2n/-1 to the doubly logarithmic quark and gluon form factors are also calculated. With these corrections taken into account the form factors are given by simple formulas.